Answer
$x=10$ or $x=5$
Work Step by Step
$ 14(x-4)-(x+2)=(x+2)(x-4)\qquad$... use the distributive property: $a(b+c)=ab+ac$.
$ 14x-56-x-2=(x+2)(x-4)\qquad$... use the FOIL method.
$ 14x-56-x-2=x^{2}-4x+2x-8\qquad$...add like terms.
$ 13x-58=x^{2}-2x-8\qquad$...add $(-x^{2}+2x+8)$ to both sides.
$ 13x-58-x^{2}+2x+8=x^{2}-2x-8-x^{2}+2x+8\qquad$...add like terms.
$-x^{2}+15x-50=0\qquad$...mulitiply both sides by $-1$.
$ x^{2}-15x+50=0\qquad$... solve with the Quadractic formula. $a=1,\ b=-15,\ c=50$
$ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-15,\ a$ for $1$ and $c$ for $50$.
$ x=\displaystyle \frac{-(-15)\pm\sqrt{(-15)^{2}-4\cdot(50)\cdot 1}}{2\cdot 1}\qquad$... simplify.
$x=\displaystyle \frac{15\pm\sqrt{225-200}}{2}$
$x=\displaystyle \frac{15\pm\sqrt{25}}{2}$
$ x=\displaystyle \frac{15\pm 5}{2}\qquad$... the symbol $\pm$ indicates two solutions.
$x=\displaystyle \frac{15+5}{2}=\frac{20}{2}=10$ or $x=\displaystyle \frac{15-5}{2}=\frac{10}{2}=5$
