How do you solve (2m + 3)(4m + 3) = 0?

Mar 14, 2018

$m = - 12 , - 6$

Explanation:

Multiply the equation using FOIL

$\left(2 m + 3\right) \left(4 m + 3\right) = 0$
$\left(2 m \cdot 4 m\right) + \left(2 m \cdot 3\right) + \left(3 \cdot 4 m\right) + \left(3 \cdot 3\right) = 0$
$8 {m}^{2} + 6 m + 12 m + 9 = 0$
$8 {m}^{2} + 18 m + 9 = 0$

Since it would be sort of difficult to factor mentally,
(or just keep plugging in factors till you get the answer)

$\frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

$\frac{- \left(18\right) \pm \sqrt{{\left(18\right)}^{2} - 4 \left(8\right) \left(9\right)}}{2 \left(8\right)}$

$\frac{- 18 \pm \sqrt{324 - 288}}{16}$

$\frac{- 18 \pm \sqrt{36}}{16}$

$\frac{- 18 \pm 6}{16}$

$\frac{- 9 \pm 3}{8} = 0$

$m = - 12 , - 6$