So with this, we are going to be factoring by grouping. Firstly, factor x³ + 3x² and -4x - 12 separately. Make sure that they have the same quantity on the inside:
[tex]x^2(x+3)-4(x+3)=0[/tex]
Now you can rewrite this equation as [tex](x^2-4)(x+3)=0[/tex] . However we are not finished yet.
With x² - 4, we will be applying the difference of squares, which is "(x² - y²) = (x + y)(x - y)". Apply this here as such:
[tex](x^2-4)=(x+2)(x-2)\\\\(x+2)(x-2)(x+3)=0[/tex]
Now apply the zero product property and solve for x:
[tex]x+2=0\\x=-2\\\\x-2=0\\x=2\\\\x+3=0\\x=-3[/tex]
Your answers are x = -2, x = 2, and x = -3.
