Answer
$x=-\frac{2}{3} \text{ or } x=4$
Work Step by Step
There is a need to factor the trinomial on the left side of the equation.
The product of the leading term (3) and the constant term (-8) is $-24$.
The factors of $-24$ whose sum is equal to the coefficient of the middle term, which is $-10$, are $2$ and $-12$.
Write the middle using these factors to have:
$\\3x^2+2x-12x-8=0$
Regroup to have:
$\\(3x^2+2x)+(-12x-8)=0$
Factor out the GCF of each group to have:
$\\x(3x+2)+(-4)(3x+2)=0
\\(3x+2)(x-4)=0$
Equate each factor to zero then solve each equation to have:
$\\3x+2=0 \text{ or } x-4=0
\\3x=-2 \text{ or } x=4
\\x=-\frac{2}{3} \text{ or } x=4$
