Greetings!
[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]
Hope this helps.
-Benjamin
