Question

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

Answer 1

x=2 and x=-2

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