Question

solve for all values of x by factoring. x^2 - 6x = -6x + 4

Explanation:

Step1: Rearrange the equation

Add $6x$ to both sides of the equation $x^{2}-6x=-6x + 4$. We get $x^{2}-6x+6x=-6x + 6x+4$, which simplifies to $x^{2}=4$.

Step2: Factor and solve

Rewrite $x^{2}-4 = 0$. Using the difference - of - squares formula $a^{2}-b^{2}=(a + b)(a - b)$, where $a=x$ and $b = 2$, we have $(x + 2)(x - 2)=0$. Then, by the zero - product property, if $ab=0$, either $a = 0$ or $b = 0$. So $x+2=0$ gives $x=-2$ and $x - 2=0$ gives $x = 2$.

Answer:

$x = 2,x=-2$