Question

{35 POINTS)What are the solutions of 2a^3-3a^2=8a-12 ?

Answer 1

Greetings!

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

Hope this helps.
-Benjamin