(x-6)(x-6)=3x-8

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Solution for (x-6)(x-6)=3x-8 equation: 


Simplifying
(x + -6)(x + -6) = 3x + -8

Reorder the terms:
(-6 + x)(x + -6) = 3x + -8

Reorder the terms:
(-6 + x)(-6 + x) = 3x + -8

Multiply (-6 + x) * (-6 + x)
(-6(-6 + x) + x(-6 + x)) = 3x + -8
((-6 * -6 + x * -6) + x(-6 + x)) = 3x + -8
((36 + -6x) + x(-6 + x)) = 3x + -8
(36 + -6x + (-6 * x + x * x)) = 3x + -8
(36 + -6x + (-6x + x2)) = 3x + -8

Combine like terms: -6x + -6x = -12x
(36 + -12x + x2) = 3x + -8

Reorder the terms:
36 + -12x + x2 = -8 + 3x

Solving
36 + -12x + x2 = -8 + 3x

Solving for variable 'x'.

Reorder the terms:
36 + 8 + -12x + -3x + x2 = -8 + 3x + 8 + -3x

Combine like terms: 36 + 8 = 44
44 + -12x + -3x + x2 = -8 + 3x + 8 + -3x

Combine like terms: -12x + -3x = -15x
44 + -15x + x2 = -8 + 3x + 8 + -3x

Reorder the terms:
44 + -15x + x2 = -8 + 8 + 3x + -3x

Combine like terms: -8 + 8 = 0
44 + -15x + x2 = 0 + 3x + -3x
44 + -15x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
44 + -15x + x2 = 0

Factor a trinomial.
(4 + -1x)(11 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {4, 11}

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