(x-4)(x-2)=5x-22

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Solution for (x-4)(x-2)=5x-22 equation: 


Simplifying
(x + -4)(x + -2) = 5x + -22

Reorder the terms:
(-4 + x)(x + -2) = 5x + -22

Reorder the terms:
(-4 + x)(-2 + x) = 5x + -22

Multiply (-4 + x) * (-2 + x)
(-4(-2 + x) + x(-2 + x)) = 5x + -22
((-2 * -4 + x * -4) + x(-2 + x)) = 5x + -22
((8 + -4x) + x(-2 + x)) = 5x + -22
(8 + -4x + (-2 * x + x * x)) = 5x + -22
(8 + -4x + (-2x + x2)) = 5x + -22

Combine like terms: -4x + -2x = -6x
(8 + -6x + x2) = 5x + -22

Reorder the terms:
8 + -6x + x2 = -22 + 5x

Solving
8 + -6x + x2 = -22 + 5x

Solving for variable 'x'.

Reorder the terms:
8 + 22 + -6x + -5x + x2 = -22 + 5x + 22 + -5x

Combine like terms: 8 + 22 = 30
30 + -6x + -5x + x2 = -22 + 5x + 22 + -5x

Combine like terms: -6x + -5x = -11x
30 + -11x + x2 = -22 + 5x + 22 + -5x

Reorder the terms:
30 + -11x + x2 = -22 + 22 + 5x + -5x

Combine like terms: -22 + 22 = 0
30 + -11x + x2 = 0 + 5x + -5x
30 + -11x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
30 + -11x + x2 = 0

Factor a trinomial.
(5 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

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 = {5, 6}

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