[tex]2a^3-3a^2=8a-12[/tex] Add -(8a-12) to both sides. [tex](2a^3-3a^2)+-(8a-12)=8a-12-(8a-12)[/tex] Simplify. [tex]2a^3-3a^2-8a+12=0[/tex] Rearrange. [tex]2a^3-8a-3a^2+12=0[/tex] Factor Out 2a. [tex]2a(a^2-4)-3a^2+12=0[/tex] Factor Out the difference of squares. [tex]2a(a-2)(a+2)-3a^2+12=0[/tex] Factor out -3. [tex]2a(a-2)(a+2)-3(a^2-4)=0[/tex] Factor Out the difference of squares. [tex]2a(a-2)(a+2)-3(a-2)(a+2)=0[/tex] Find Common Factor. [tex](a+2)(a-2)(2a-3)=0[/tex] Set Factors to Equal 0. [tex](a+2)=0 \\ \\ (a-2)=0 \\ \\ (2a-3)=0[/tex] [tex]a=-2 \\ \\ a=2 \\ \\ a=3/2[/tex]
