Question

Solve for all values of x by factoring.
x² - 6x = -6x +4

Answer 1

Answer:

x=2 and x=-2

Step-by-step explanation:

Original Equation:

$x^2-6x=-6x+4$

Add 6x to both sides

$x^2=4$

Subtract 4 from both sides

$x^2-4=0$

Use difference of squares: $a^2-b^2=(a-b)(a+b)$

$(x-2)(x+2)=0$

Since the factors are being multiplied by each other, if one of the factors is equal to zero, then the entire thing becomes zero, since 0 * anything = 0

So to find the values of x that satisfy this equation, set each factor equal to zero

$x-2=0$

Add 2 to both sides

$x=2$

$x+2=0$

subtract 2 from both sides

$x=-2$

We have both values that satisfy this equation, x=2 and x=-2