Solve by factoring and using the principle of zero products.
-$6 d^{2}+13 d+6=0$
A) $-\frac{3}{2},-\frac{2}{3}$
B) $-\frac{2}{3},-\frac{2}{3}$
C) $\frac{2}{3}, \frac{3}{2}$
D) $\frac{3}{2}, \frac{2}{3}$

Question

Quizplus · Accepted Answer

To solve the quadratic equation $6d^2 + 13d + 6 = 0$ by factoring, we look for two numbers that multiply to $6*6=36$ and add to $13$. These numbers are $9$ and $4$, so we can rewrite the middle term $13d$ as $9d + 4d$, giving us $6d^2 + 9d + 4d + 6 = 0$. Factoring by grouping, we get $3d(2d + 3) + 2(2d + 3) = 0$, which simplifies to $(3d + 2)(2d + 3) = 0$. Setting each factor equal to zero gives us $3d + 2 = 0$ and $2d + 3 = 0$, leading to $d = -\frac{2}{3}$ and $d = -\frac{3}{2}$, respectively.

Solve by Factoring and Using the Principle of Zero Products 6d2+13d+6=06 d^{2}+13 d+6=06d2+13d+6=0

Solve by Factoring and Using the Principle of Zero Products $6 d^{2}+13 d+6=0$