solve for all values of $x$ by factoring.\n$x^{2}+6x - 64 = 6x$

Explanation:

Step1: Rearrange the equation

Subtract $6x$ from both sides of the equation $x^{2}+6x - 64=6x$. $x^{2}+6x-6x - 64=6x-6x$ $x^{2}-64 = 0$

Step2: Factor using difference - of - squares

Recall the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$. Here $a = x$ and $b = 8$. $x^{2}-64=(x + 8)(x - 8)=0$

Step3: Solve for $x$

Set each factor equal to zero. If $x + 8=0$, then $x=-8$. If $x - 8=0$, then $x = 8$.

Answer:

$x=-8,8$