Solve for all values of x by factoring

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

To solve the equation by factoring, we need to rewrite both sides of the equation in factored form.

Starting with the left side:
x^2 - 6x

We notice that there is a common factor of x:
x(x - 6)

Now, let's focus on the right side:
-6x + 4

We can rewrite this as:
4 - 6x

Now, we can set the factored expressions equal to each other and solve for x:
x(x - 6) = 4 - 6x

Expanding the left side:
x^2 - 6x = 4 - 6x

Adding 6x to both sides:
x^2 = 4

Taking the square root of both sides:
x = ±2

Therefore, the equation has two solutions, x = 2 and x = -2.