Solve the Quadratic Equation by Factorization: 3x² = −11x − 10

Question: Solve the following quadratic equation by factorization:

$$ 3x^2=-11x-10 $$

Solution

$$ 3x^2+11x+10=0 $$

$$ 3x^2+6x+5x+10=0 $$

$$ 3x(x+2)+5(x+2)=0 $$

$$ (x+2)(3x+5)=0 $$

Either

$$ x+2=0 $$

$$ x=-2 $$

or

$$ 3x+5=0 $$

$$ x=-\frac{5}{3} $$

Hence,

$$ \boxed{x=-2,\ -\frac{5}{3}} $$