(x-7)(x-6)=3x-22

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Solution for (x-7)(x-6)=3x-22 equation: 


Simplifying
(x + -7)(x + -6) = 3x + -22

Reorder the terms:
(-7 + x)(x + -6) = 3x + -22

Reorder the terms:
(-7 + x)(-6 + x) = 3x + -22

Multiply (-7 + x) * (-6 + x)
(-7(-6 + x) + x(-6 + x)) = 3x + -22
((-6 * -7 + x * -7) + x(-6 + x)) = 3x + -22
((42 + -7x) + x(-6 + x)) = 3x + -22
(42 + -7x + (-6 * x + x * x)) = 3x + -22
(42 + -7x + (-6x + x2)) = 3x + -22

Combine like terms: -7x + -6x = -13x
(42 + -13x + x2) = 3x + -22

Reorder the terms:
42 + -13x + x2 = -22 + 3x

Solving
42 + -13x + x2 = -22 + 3x

Solving for variable 'x'.

Reorder the terms:
42 + 22 + -13x + -3x + x2 = -22 + 3x + 22 + -3x

Combine like terms: 42 + 22 = 64
64 + -13x + -3x + x2 = -22 + 3x + 22 + -3x

Combine like terms: -13x + -3x = -16x
64 + -16x + x2 = -22 + 3x + 22 + -3x

Reorder the terms:
64 + -16x + x2 = -22 + 22 + 3x + -3x

Combine like terms: -22 + 22 = 0
64 + -16x + x2 = 0 + 3x + -3x
64 + -16x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
64 + -16x + x2 = 0

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


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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {8, 8}

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