If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Solving quadratics by factoring review

Factoring quadratics makes it easier to find their solutions. This article reviews factoring techniques and gives you a chance to try some practice problems.

### Example 1

Find the solutions of the equation.
$2{x}^{2}-3x-20={x}^{2}+34$

$\begin{array}{rl}2{x}^{2}-3x-20& ={x}^{2}+34\\ \\ 2{x}^{2}-3x-20-{x}^{2}-34& =0\\ \\ {x}^{2}-3x-54& =0\\ \\ \left(x+6\right)\left(x-9\right)& =0\end{array}$
$\begin{array}{rlr}& ↙& ↘\\ \\ x+6& =0& x-9& =0\\ \\ x& =-6& x& =9\end{array}$
In conclusion, the solutions are $x=-6$ and $x=9$.
Want to see see another example? Check out this video.

### Example 2

Find the solutions of the equation.
$3{x}^{2}+33x+30=0$

$\begin{array}{rl}3{x}^{2}+33x+30& =0\\ \\ {x}^{2}+11x+10& =0\\ \\ \left(x+1\right)\left(x+10\right)& =0\end{array}$
$\begin{array}{rlr}& ↙& ↘\\ \\ x+1& =0& x+10& =0\\ \\ x& =-1& x& =-10\end{array}$
In conclusion, the solutions are $x=-1$ and $x=-10$.
Want to see see another example? Check out this video.

### Example 3

Find the solutions of the equation.
$3{x}^{2}-9x-20={x}^{2}+5x+16$

$\begin{array}{rl}3{x}^{2}-9x-20& ={x}^{2}+5x+16\\ \\ 3{x}^{2}-9x-20-{x}^{2}-5x-16& =0\\ \\ 2{x}^{2}-14x-36& =0\\ \\ {x}^{2}-7x-18& =0\\ \\ \left(x+2\right)\left(x-9\right)& =0\end{array}$
$\begin{array}{rlr}& ↙& ↘\\ \\ x+2& =0& x-9& =0\\ \\ x& =-2& x& =9\end{array}$
In conclusion, the solutions are $x=-2$ and $x=9$.
Want to see see another example? Check out this video.

## Practice

Problem 1
Solve for $x$.
${x}^{2}+14x+49=0$
$x=$

Want more practice? Check out these exercises: