(x-7)(x-7)=(9-x)(9-x)

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Solution for (x-7)(x-7)=(9-x)(9-x) equation: 


Simplifying
(x + -7)(x + -7) = (9 + -1x)(9 + -1x)

Reorder the terms:
(-7 + x)(x + -7) = (9 + -1x)(9 + -1x)

Reorder the terms:
(-7 + x)(-7 + x) = (9 + -1x)(9 + -1x)

Multiply (-7 + x) * (-7 + x)
(-7(-7 + x) + x(-7 + x)) = (9 + -1x)(9 + -1x)
((-7 * -7 + x * -7) + x(-7 + x)) = (9 + -1x)(9 + -1x)
((49 + -7x) + x(-7 + x)) = (9 + -1x)(9 + -1x)
(49 + -7x + (-7 * x + x * x)) = (9 + -1x)(9 + -1x)
(49 + -7x + (-7x + x2)) = (9 + -1x)(9 + -1x)

Combine like terms: -7x + -7x = -14x
(49 + -14x + x2) = (9 + -1x)(9 + -1x)

Multiply (9 + -1x) * (9 + -1x)
49 + -14x + x2 = (9(9 + -1x) + -1x * (9 + -1x))
49 + -14x + x2 = ((9 * 9 + -1x * 9) + -1x * (9 + -1x))
49 + -14x + x2 = ((81 + -9x) + -1x * (9 + -1x))
49 + -14x + x2 = (81 + -9x + (9 * -1x + -1x * -1x))
49 + -14x + x2 = (81 + -9x + (-9x + 1x2))

Combine like terms: -9x + -9x = -18x
49 + -14x + x2 = (81 + -18x + 1x2)

Solving
49 + -14x + x2 = 81 + -18x + 1x2

Solving for variable 'x'.

Reorder the terms:
49 + -81 + -14x + 18x + x2 + -1x2 = 81 + -18x + 1x2 + -81 + 18x + -1x2

Combine like terms: 49 + -81 = -32
-32 + -14x + 18x + x2 + -1x2 = 81 + -18x + 1x2 + -81 + 18x + -1x2

Combine like terms: -14x + 18x = 4x
-32 + 4x + x2 + -1x2 = 81 + -18x + 1x2 + -81 + 18x + -1x2

Combine like terms: x2 + -1x2 = 0
-32 + 4x + 0 = 81 + -18x + 1x2 + -81 + 18x + -1x2
-32 + 4x = 81 + -18x + 1x2 + -81 + 18x + -1x2

Reorder the terms:
-32 + 4x = 81 + -81 + -18x + 18x + 1x2 + -1x2

Combine like terms: 81 + -81 = 0
-32 + 4x = 0 + -18x + 18x + 1x2 + -1x2
-32 + 4x = -18x + 18x + 1x2 + -1x2

Combine like terms: -18x + 18x = 0
-32 + 4x = 0 + 1x2 + -1x2
-32 + 4x = 1x2 + -1x2

Combine like terms: 1x2 + -1x2 = 0
-32 + 4x = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-8 + x) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

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

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Solution
x = {8}

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