To solve this trigonometric equation, we can use the sum and difference formulas for sine and cosine.

Using the sum and difference formulas, we have:
sin$3x$ cos$2x$ = sin$3x+2x$ = sin$5x$ sin$2x$ cos$3x$ = sin$2x+3x$ = sin$5x$

Therefore, sin$3x$ cos$2x$ = sin$2x$ cos$3x$ when 5x = 0 + n2π or 5x = π + n2π, where n is an integer.