Expanding the left side of the equation:

(x-1)(x^2+6x+9) = x(x^2+6x+9) - 1(x^2+6x+9)
= x^3 + 6x^2 + 9x - x^2 - 6x - 9
= x^3 + 5x^2 + 3x - 9

Expanding the right side of the equation:

5(x+3) = 5x + 15

Setting the two sides equal to each other:

x^3 + 5x^2 + 3x - 9 = 5x + 15

Rearranging terms:

x^3 + 5x^2 + 3x - 5x - 15 - 9 = 0
x^3 + 5x^2 - 2x - 24 = 0

This is the final equation.