To find the equation for the supplementary angles \(\angle ABC\) and \(\angle CBD\), we start by using the fact that supplementary angles add up to \(180^\circ\).
We know:
- \(\angle ABC = (3x + 25)^\circ\)
- \(\angle CBD = 32^\circ\)
Since these angles are supplementary, we can write the equation as:
\[ (3x + 25) + 32 = 180 \]
Now, simplify the equation:
\[ 3x + 25 + 32 = 180 \]
Combine the constant terms:
\[ 3x + 57 = 180 \]
This is the equation in simplest terms to solve for \(x\):
\[ 3x + 57 = 180 \]