Solve the Quadratic Equation by Factorization: ax² + (4a² − 3b)x − 12ab = 0

Question: Solve the following quadratic equation by factorization:

$$ ax^2+(4a^2-3b)x-12ab=0 $$

Solution

$$ ax^2+4a^2x-3bx-12ab=0 $$

$$ ax(x+4a)-3b(x+4a)=0 $$

$$ (x+4a)(ax-3b)=0 $$

Either

$$ x+4a=0 $$

$$ x=-4a $$

or

$$ ax-3b=0 $$

$$ x=\frac{3b}{a} $$

Hence,

$$ \boxed{x=-4a,\ \frac{3b}{a}} $$