Question

solve for u.
3u² + 10u - 13 = 0
write each solution as an integer, proper fraction, or improper fraction in simplest form.
if there are multiple solutions, separate them with commas.
u =

Explanation:

Step1: Factor the quadratic equation

We factor $3u^{2}+10u - 13=0$. We need to find two numbers that multiply to $3\times(- 13)=-39$ and add up to $10$. The numbers are $13$ and $-3$. So we can rewrite the middle - term: $3u^{2}+13u-3u - 13 = 0$. Then factor by grouping: $u(3u + 13)-1(3u + 13)=0$, which gives $(3u + 13)(u - 1)=0$.

Step2: Set each factor equal to zero

Set $3u+13 = 0$ and $u - 1=0$.
For $3u+13 = 0$, we solve for $u$:
$3u=-13$, so $u=-\frac{13}{3}$.
For $u - 1=0$, we solve for $u$:
$u = 1$.

Answer:

$1,-\frac{13}{3}$