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

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


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

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

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

Multiply (8 + 9x) * (-6 + x)
(8(-6 + x) + 9x * (-6 + x)) = (x + -8)(x + -6)
((-6 * 8 + x * 8) + 9x * (-6 + x)) = (x + -8)(x + -6)
((-48 + 8x) + 9x * (-6 + x)) = (x + -8)(x + -6)
(-48 + 8x + (-6 * 9x + x * 9x)) = (x + -8)(x + -6)
(-48 + 8x + (-54x + 9x2)) = (x + -8)(x + -6)

Combine like terms: 8x + -54x = -46x
(-48 + -46x + 9x2) = (x + -8)(x + -6)

Reorder the terms:
-48 + -46x + 9x2 = (-8 + x)(x + -6)

Reorder the terms:
-48 + -46x + 9x2 = (-8 + x)(-6 + x)

Multiply (-8 + x) * (-6 + x)
-48 + -46x + 9x2 = (-8(-6 + x) + x(-6 + x))
-48 + -46x + 9x2 = ((-6 * -8 + x * -8) + x(-6 + x))
-48 + -46x + 9x2 = ((48 + -8x) + x(-6 + x))
-48 + -46x + 9x2 = (48 + -8x + (-6 * x + x * x))
-48 + -46x + 9x2 = (48 + -8x + (-6x + x2))

Combine like terms: -8x + -6x = -14x
-48 + -46x + 9x2 = (48 + -14x + x2)

Solving
-48 + -46x + 9x2 = 48 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
-48 + -48 + -46x + 14x + 9x2 + -1x2 = 48 + -14x + x2 + -48 + 14x + -1x2

Combine like terms: -48 + -48 = -96
-96 + -46x + 14x + 9x2 + -1x2 = 48 + -14x + x2 + -48 + 14x + -1x2

Combine like terms: -46x + 14x = -32x
-96 + -32x + 9x2 + -1x2 = 48 + -14x + x2 + -48 + 14x + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
-96 + -32x + 8x2 = 48 + -14x + x2 + -48 + 14x + -1x2

Reorder the terms:
-96 + -32x + 8x2 = 48 + -48 + -14x + 14x + x2 + -1x2

Combine like terms: 48 + -48 = 0
-96 + -32x + 8x2 = 0 + -14x + 14x + x2 + -1x2
-96 + -32x + 8x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-96 + -32x + 8x2 = 0 + x2 + -1x2
-96 + -32x + 8x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-96 + -32x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-12 + -4x + x2) = 0

Factor a trinomial.
8((-2 + -1x)(6 + -1x)) = 0

Ignore the factor 8.

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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2, 6}

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