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

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


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

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

Solving
-4x + x2 = 8 + -2x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-2 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2, 4}

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