Answer
$3(x+3)(x-2)$
Work Step by Step
$3x^{2}+3x-6=$
...factor out the GCF.
$=3(x^{2}+x-6)$
...find factors of $ac$ with a sum of $b$.
($ac=-6,\ b=1$)
$\left[\begin{array}{lll}
\text{Factors of -6} & \text{Sum of factors} & \\
1\text{ and }-6 & -5 & \\
-1\text{ and }6 & 5 & \\
2\text{ and }-3 & -1 & \\
-2\text{ and }3 & 1 & \text{ is what we need }
\end{array}\right]$
...use the factors you found to rewrite $bx$.
$=3(x^{2}-2x+3x-6)$
...factor by grouping.
$=3[x(x-2)+3(x-2)]$
...factor again.
$=3(x+3)(x-2)$
