Answer:
The solutions to the equation are -3,-2,2
Step-by-step explanation:
x^3+3x^2=4x+12
Subtract 4x +12 from each side
x^3+3x^2-4x-12=4x+12-4x-12
x^3+3x^2-4x-12=0
I will use factoring by grouping
x^3+3x^2 -4x-12=0
I will factor out x^2 from the first group and -4 from the second group
x^2 (x+3) -4(x+3) =0
Now we can factor out (x+3)
(x+3) (x^2-4) =0
We can use the zero product principle since the right hand side is equal to 0
x+3 =0 x^2-4 =0
x+3-3=0-3 x^2 -4+4=0+4
x=-3 x^2=4
Take the square root of each side
sqrt(x^2) = sqrt(4)
x=±2
The solutions to the equation are -3,-2,2
