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

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


Simplifying
4(2 + -1x) = (2 + -1x)(x + 2)
(2 * 4 + -1x * 4) = (2 + -1x)(x + 2)
(8 + -4x) = (2 + -1x)(x + 2)

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

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

Combine like terms: 2x + -2x = 0
8 + -4x = (4 + 0 + -1x2)
8 + -4x = (4 + -1x2)

Solving
8 + -4x = 4 + -1x2

Solving for variable 'x'.

Reorder the terms:
8 + -4 + -4x + x2 = 4 + -1x2 + -4 + x2

Combine like terms: 8 + -4 = 4
4 + -4x + x2 = 4 + -1x2 + -4 + x2

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

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

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

Factor a trinomial.
(2 + -1x)(2 + -1x) = 0


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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {2, 2}

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