Solve x^3+5x^2=9x+45

Minus (9x+45) both sides

x³+5x²-9x-45=0

group and factor

(x³+5x²) + (-9x-45) = 0

factor

x² (x+5) - 9 (x+5) = 0

undistribute

(x²-9) (x+5) = 0

factor difference of 2 perfect squares

(x-3) (x+3) (x+5) = 0

set to zero

x-3=0

x=3

x+3=0

x=-3

x+5=0

x=-5

x=-5, and - 3 and 3