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