(x+4)(x-4)=(5-x)(4-x)

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Solution for (x+4)(x-4)=(5-x)(4-x) equation: 


Simplifying
(x + 4)(x + -4) = (5 + -1x)(4 + -1x)

Reorder the terms:
(4 + x)(x + -4) = (5 + -1x)(4 + -1x)

Reorder the terms:
(4 + x)(-4 + x) = (5 + -1x)(4 + -1x)

Multiply (4 + x) * (-4 + x)
(4(-4 + x) + x(-4 + x)) = (5 + -1x)(4 + -1x)
((-4 * 4 + x * 4) + x(-4 + x)) = (5 + -1x)(4 + -1x)
((-16 + 4x) + x(-4 + x)) = (5 + -1x)(4 + -1x)
(-16 + 4x + (-4 * x + x * x)) = (5 + -1x)(4 + -1x)
(-16 + 4x + (-4x + x2)) = (5 + -1x)(4 + -1x)

Combine like terms: 4x + -4x = 0
(-16 + 0 + x2) = (5 + -1x)(4 + -1x)
(-16 + x2) = (5 + -1x)(4 + -1x)

Multiply (5 + -1x) * (4 + -1x)
-16 + x2 = (5(4 + -1x) + -1x * (4 + -1x))
-16 + x2 = ((4 * 5 + -1x * 5) + -1x * (4 + -1x))
-16 + x2 = ((20 + -5x) + -1x * (4 + -1x))
-16 + x2 = (20 + -5x + (4 * -1x + -1x * -1x))
-16 + x2 = (20 + -5x + (-4x + 1x2))

Combine like terms: -5x + -4x = -9x
-16 + x2 = (20 + -9x + 1x2)

Solving
-16 + x2 = 20 + -9x + 1x2

Solving for variable 'x'.

Reorder the terms:
-16 + -20 + 9x + x2 + -1x2 = 20 + -9x + 1x2 + -20 + 9x + -1x2

Combine like terms: -16 + -20 = -36
-36 + 9x + x2 + -1x2 = 20 + -9x + 1x2 + -20 + 9x + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 9x + 0 = 20 + -9x + 1x2 + -20 + 9x + -1x2
-36 + 9x = 20 + -9x + 1x2 + -20 + 9x + -1x2

Reorder the terms:
-36 + 9x = 20 + -20 + -9x + 9x + 1x2 + -1x2

Combine like terms: 20 + -20 = 0
-36 + 9x = 0 + -9x + 9x + 1x2 + -1x2
-36 + 9x = -9x + 9x + 1x2 + -1x2

Combine like terms: -9x + 9x = 0
-36 + 9x = 0 + 1x2 + -1x2
-36 + 9x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-36 + 9x = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-4 + x) = 0

Ignore the factor 9.

Subproblem 1
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 = {4}

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