I have a simple problem, but I'm new to Silverlight.
I have a textbox, transparent, but when I got focus, textfield background will come white.
How to solve?

You just need to either edit the "FocusedState" in the VisualStateManager for the Default control template, or provide your own like the one provided below in either a Resource Dictionary or in your UserControl.Resources etc.
Here's how you would apply the Style Template Below to your TextBox Instance
<TextBox Style="{StaticResource YourCustomTextBoxStyle}/>
Here's a Default WP7 TextBox Style Template with the proper place Adjusted...
<Style x:Key="YourCustomTextBoxStyle" TargetType="TextBox">
<Setter Property="FontFamily" Value="{StaticResource PhoneFontFamilyNormal}"/>
<Setter Property="FontSize" Value="{StaticResource PhoneFontSizeMediumLarge}"/>
<Setter Property="Background" Value="{StaticResource PhoneTextBoxBrush}"/>
<Setter Property="Foreground" Value="{StaticResource PhoneTextBoxForegroundBrush}"/>
<Setter Property="BorderBrush" Value="{StaticResource PhoneTextBoxBrush}"/>
<Setter Property="SelectionBackground" Value="{StaticResource PhoneAccentBrush}"/>
<Setter Property="SelectionForeground" Value="{StaticResource PhoneTextBoxSelectionForegroundBrush}"/>
<Setter Property="BorderThickness" Value="{StaticResource PhoneBorderThickness}"/>
<Setter Property="Padding" Value="2"/>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="TextBox">
<Grid Background="Transparent">
<VisualStateManager.VisualStateGroups>
<VisualStateGroup x:Name="CommonStates">
<VisualState x:Name="Normal"/>
<VisualState x:Name="MouseOver"/>
<VisualState x:Name="Disabled">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="EnabledBorder">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Collapsed</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="DisabledOrReadonlyBorder">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
<VisualState x:Name="ReadOnly">
<Storyboard>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="EnabledBorder">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Collapsed</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Visibility" Storyboard.TargetName="DisabledOrReadonlyBorder">
<DiscreteObjectKeyFrame KeyTime="0">
<DiscreteObjectKeyFrame.Value>
<Visibility>Visible</Visibility>
</DiscreteObjectKeyFrame.Value>
</DiscreteObjectKeyFrame>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Background" Storyboard.TargetName="DisabledOrReadonlyBorder">
<DiscreteObjectKeyFrame KeyTime="0" Value="{StaticResource PhoneTextBoxBrush}"/>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="BorderBrush" Storyboard.TargetName="DisabledOrReadonlyBorder">
<DiscreteObjectKeyFrame KeyTime="0" Value="{StaticResource PhoneTextBoxBrush}"/>
</ObjectAnimationUsingKeyFrames>
<ObjectAnimationUsingKeyFrames Storyboard.TargetProperty="Foreground" Storyboard.TargetName="DisabledOrReadonlyContent">
<DiscreteObjectKeyFrame KeyTime="0" Value="{StaticResource PhoneTextBoxReadOnlyBrush}"/>
</ObjectAnimationUsingKeyFrames>
</Storyboard>
</VisualState>
</VisualStateGroup>
<VisualStateGroup x:Name="FocusStates">
<VisualState x:Name="Focused"/> <!-- *** Right here is your culprit, I just ripped out the FocusedState Storyboard so it doesnt do anything when focused. *** -->
<VisualState x:Name="Unfocused"/>
</VisualStateGroup>
</VisualStateManager.VisualStateGroups>
<Border x:Name="EnabledBorder" BorderBrush="{TemplateBinding BorderBrush}" BorderThickness="{TemplateBinding BorderThickness}" Background="{TemplateBinding Background}" Margin="{StaticResource PhoneTouchTargetOverhang}">
<ContentControl x:Name="ContentElement" BorderThickness="0" HorizontalContentAlignment="Stretch" Margin="{StaticResource PhoneTextBoxInnerMargin}" Padding="{TemplateBinding Padding}" VerticalContentAlignment="Stretch"/>
</Border>
<Border x:Name="DisabledOrReadonlyBorder" BorderBrush="{StaticResource PhoneDisabledBrush}" BorderThickness="{TemplateBinding BorderThickness}" Background="Transparent" Margin="{StaticResource PhoneTouchTargetOverhang}" Visibility="Collapsed">
<TextBox x:Name="DisabledOrReadonlyContent" Background="Transparent" Foreground="{StaticResource PhoneDisabledBrush}" FontWeight="{TemplateBinding FontWeight}" FontStyle="{TemplateBinding FontStyle}" FontSize="{TemplateBinding FontSize}" FontFamily="{TemplateBinding FontFamily}" IsReadOnly="True" SelectionForeground="{TemplateBinding SelectionForeground}" SelectionBackground="{TemplateBinding SelectionBackground}" TextAlignment="{TemplateBinding TextAlignment}" TextWrapping="{TemplateBinding TextWrapping}" Text="{TemplateBinding Text}" Template="{StaticResource PhoneDisabledTextBoxTemplate}"/>
</Border>
</Grid>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
You can also apply this same template to all your TextBox controls by default utilizing BasedOn Values.
There's other ways of doing this with less but this is a good place to begin learning the fundamentals. Hope it helps.
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