Solve for all values of xx by factoring.x, squared, minus, 8, x, plus, 8, equals, minus, 4x 2 −8x+8=−4

The equation you've given is x^2 - 8x + 8 = -4.

First, let's simplify the equation by adding 4 to both sides to set the equation to equal zero:

x^2 - 8x + 8 + 4 = 0

This simplifies to:

x^2 - 8x + 12 = 0

Next, we factor the quadratic equation. We're looking for two numbers that multiply to 12 and add to -8. Those numbers are -2 and -6. So, we can write the equation as:

(x - 2)(x - 6) = 0

Setting each factor equal to zero gives the solutions to the equation:

x - 2 = 0 => x = 2

x - 6 = 0 => x = 6

So, the solutions to the equation x^2 - 8x + 12 = 0 are x = 2 and x = 6.