Question

solve for g.
3g² + 22g - 16 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form. if there are multiple solutions, separate them with commas.
g =

Explanation:

Step1: Factor the quadratic equation

We need to factor $3g^{2}+22g - 16=0$. We look for two numbers that multiply to $3\times(-16)=- 48$ and add up to 22. The numbers are 24 and - 2. So we can rewrite the middle - term: $3g^{2}+24g-2g - 16 = 0$. Then factor by grouping: $3g(g + 8)-2(g + 8)=0$, which gives $(3g - 2)(g + 8)=0$.

Step2: Set each factor equal to zero

If $3g-2 = 0$, then $3g=2$, and $g=\frac{2}{3}$. If $g + 8=0$, then $g=-8$.

Answer:

$g=-8,\frac{2}{3}$