To solve for \( x \) given that the angles \( \angle ABC \) and \( \angle CBD \) are supplementary, we start with the understanding that supplementary angles add up to \( 180^\circ \).
Given: \[ \angle ABC = 3x + 25 \] \[ \angle CBD = 32 \]
We set up the equation using the fact that these angles are supplementary: \[ (3x + 25) + 32 = 180 \]
Now, combine like terms: \[ 3x + 25 + 32 = 180 \] \[ 3x + 57 = 180 \]
To express this in the simplest term as you requested, we can rewrite it as: \[ 3x + 57 = 180 \]
Thus, the equation to solve for \( x \) in the required format is: \[ 3x + 57 = 180 \]