Question

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

Answer 1

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