(2x-6)(2x-6)=(9x+8)(x-8)

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Solution for (2x-6)(2x-6)=(9x+8)(x-8) equation: 


Simplifying
(2x + -6)(2x + -6) = (9x + 8)(x + -8)

Reorder the terms:
(-6 + 2x)(2x + -6) = (9x + 8)(x + -8)

Reorder the terms:
(-6 + 2x)(-6 + 2x) = (9x + 8)(x + -8)

Multiply (-6 + 2x) * (-6 + 2x)
(-6(-6 + 2x) + 2x * (-6 + 2x)) = (9x + 8)(x + -8)
((-6 * -6 + 2x * -6) + 2x * (-6 + 2x)) = (9x + 8)(x + -8)
((36 + -12x) + 2x * (-6 + 2x)) = (9x + 8)(x + -8)
(36 + -12x + (-6 * 2x + 2x * 2x)) = (9x + 8)(x + -8)
(36 + -12x + (-12x + 4x2)) = (9x + 8)(x + -8)

Combine like terms: -12x + -12x = -24x
(36 + -24x + 4x2) = (9x + 8)(x + -8)

Reorder the terms:
36 + -24x + 4x2 = (8 + 9x)(x + -8)

Reorder the terms:
36 + -24x + 4x2 = (8 + 9x)(-8 + x)

Multiply (8 + 9x) * (-8 + x)
36 + -24x + 4x2 = (8(-8 + x) + 9x * (-8 + x))
36 + -24x + 4x2 = ((-8 * 8 + x * 8) + 9x * (-8 + x))
36 + -24x + 4x2 = ((-64 + 8x) + 9x * (-8 + x))
36 + -24x + 4x2 = (-64 + 8x + (-8 * 9x + x * 9x))
36 + -24x + 4x2 = (-64 + 8x + (-72x + 9x2))

Combine like terms: 8x + -72x = -64x
36 + -24x + 4x2 = (-64 + -64x + 9x2)

Solving
36 + -24x + 4x2 = -64 + -64x + 9x2

Solving for variable 'x'.

Reorder the terms:
36 + 64 + -24x + 64x + 4x2 + -9x2 = -64 + -64x + 9x2 + 64 + 64x + -9x2

Combine like terms: 36 + 64 = 100
100 + -24x + 64x + 4x2 + -9x2 = -64 + -64x + 9x2 + 64 + 64x + -9x2

Combine like terms: -24x + 64x = 40x
100 + 40x + 4x2 + -9x2 = -64 + -64x + 9x2 + 64 + 64x + -9x2

Combine like terms: 4x2 + -9x2 = -5x2
100 + 40x + -5x2 = -64 + -64x + 9x2 + 64 + 64x + -9x2

Reorder the terms:
100 + 40x + -5x2 = -64 + 64 + -64x + 64x + 9x2 + -9x2

Combine like terms: -64 + 64 = 0
100 + 40x + -5x2 = 0 + -64x + 64x + 9x2 + -9x2
100 + 40x + -5x2 = -64x + 64x + 9x2 + -9x2

Combine like terms: -64x + 64x = 0
100 + 40x + -5x2 = 0 + 9x2 + -9x2
100 + 40x + -5x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
100 + 40x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(20 + 8x + -1x2) = 0

Factor a trinomial.
5((10 + -1x)(2 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

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

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {10, -2}

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