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

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


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

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

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

Combine like terms: 4x + -4x = 0
-4x + x2 = (16 + 0 + -1x2)
-4x + x2 = (16 + -1x2)

Solving
-4x + x2 = 16 + -1x2

Solving for variable 'x'.

Reorder the terms:
-16 + -4x + x2 + x2 = 16 + -1x2 + -16 + x2

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

Reorder the terms:
-16 + -4x + 2x2 = 16 + -16 + -1x2 + x2

Combine like terms: 16 + -16 = 0
-16 + -4x + 2x2 = 0 + -1x2 + x2
-16 + -4x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-16 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -2x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 2.

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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