0=(2x-4)*(2-x)+x^2-4x+8

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Solution for 0=(2x-4)*(2-x)+x^2-4x+8 equation: 


Simplifying
0 = (2x + -4)(2 + -1x) + x2 + -4x + 8

Reorder the terms:
0 = (-4 + 2x)(2 + -1x) + x2 + -4x + 8

Multiply (-4 + 2x) * (2 + -1x)
0 = (-4(2 + -1x) + 2x * (2 + -1x)) + x2 + -4x + 8
0 = ((2 * -4 + -1x * -4) + 2x * (2 + -1x)) + x2 + -4x + 8
0 = ((-8 + 4x) + 2x * (2 + -1x)) + x2 + -4x + 8
0 = (-8 + 4x + (2 * 2x + -1x * 2x)) + x2 + -4x + 8
0 = (-8 + 4x + (4x + -2x2)) + x2 + -4x + 8

Combine like terms: 4x + 4x = 8x
0 = (-8 + 8x + -2x2) + x2 + -4x + 8

Reorder the terms:
0 = -8 + 8 + 8x + -4x + -2x2 + x2

Combine like terms: -8 + 8 = 0
0 = 0 + 8x + -4x + -2x2 + x2
0 = 8x + -4x + -2x2 + x2

Combine like terms: 8x + -4x = 4x
0 = 4x + -2x2 + x2

Combine like terms: -2x2 + x2 = -1x2
0 = 4x + -1x2

Solving
0 = 4x + -1x2

Solving for variable 'x'.
Remove the zero:
-4x + x2 = 4x + -1x2 + -4x + x2

Reorder the terms:
-4x + x2 = 4x + -4x + -1x2 + x2

Combine like terms: 4x + -4x = 0
-4x + x2 = 0 + -1x2 + x2
-4x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-4x + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-4 + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Solution
x = {0, 4}

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