(4-x)(4-x)=x-2

Solution for (4-x)(4-x)=x-2 equation:

Simplifying
(4 + -1x)(4 + -1x) = x + -2

Multiply (4 + -1x) * (4 + -1x)
(4(4 + -1x) + -1x * (4 + -1x)) = x + -2
((4 * 4 + -1x * 4) + -1x * (4 + -1x)) = x + -2
((16 + -4x) + -1x * (4 + -1x)) = x + -2
(16 + -4x + (4 * -1x + -1x * -1x)) = x + -2
(16 + -4x + (-4x + 1x2)) = x + -2

Combine like terms: -4x + -4x = -8x
(16 + -8x + 1x2) = x + -2

Reorder the terms:
16 + -8x + 1x2 = -2 + x

Solving
16 + -8x + 1x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
16 + 2 + -8x + -1x + 1x2 = -2 + x + 2 + -1x

Combine like terms: 16 + 2 = 18
18 + -8x + -1x + 1x2 = -2 + x + 2 + -1x

Combine like terms: -8x + -1x = -9x
18 + -9x + 1x2 = -2 + x + 2 + -1x

Reorder the terms:
18 + -9x + 1x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
18 + -9x + 1x2 = 0 + x + -1x
18 + -9x + 1x2 = x + -1x

Combine like terms: x + -1x = 0
18 + -9x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {3, 6}