Question

solve the equation by factoring.
$4x^2 + 13x - 75 = 0$
$x = \square$
(simplify your answer. use a comma to separate answers as needed.)

Explanation:

Step1: Split middle term

Find two numbers that multiply to $4\times(-75)=-300$ and add to 13: 25 and -12.
Rewrite the equation: $4x^2 + 25x - 12x - 75 = 0$

Step2: Factor by grouping

Group terms and factor out GCFs:
$x(4x + 25) - 3(4x + 25) = 0$
Factor out $(4x+25)$: $(4x + 25)(x - 3) = 0$

Step3: Solve for x

Set each factor equal to 0:

1. $4x + 25 = 0 \implies 4x = -25 \implies x = -\frac{25}{4}$
2. $x - 3 = 0 \implies x = 3$

Answer:

$3, -\frac{25}{4}$