# 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.
$2x^2-3x-20=x^2+34$

\begin{aligned}2x^2-3x-20&=x^2+34\\\\ 2x^2-3x-20-x^2-34&=0\\\\ x^2-3x-54&=0\\\\ (x+6)(x-9)&=0\end{aligned}
\begin{aligned}&\swarrow&\searrow\\\\ x+6&=0&x-9&=0\\\\ x&=-6&x&=9\end{aligned}
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.
$3x^2+33x+30=0$

\begin{aligned}3x^2+33x+30&=0\\\\ x^2+11x+10&=0\\\\ (x+1)(x+10)&=0 \end{aligned}
\begin{aligned}&\swarrow&\searrow\\\\ x+1&=0&x+10&=0\\\\ x&=-1&x&=-10\end{aligned}
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.
$3x^2-9x-20=x^2+5x+16$

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

## Practice

Want more practice? Check out these exercises: