how to solve polynomial by factoring and using the zero product principle for x^3+3x^2=4x+12

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