(x-11)(x-12)=-20x+172

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Solution for (x-11)(x-12)=-20x+172 equation: 


Simplifying
(x + -11)(x + -12) = -20x + 172

Reorder the terms:
(-11 + x)(x + -12) = -20x + 172

Reorder the terms:
(-11 + x)(-12 + x) = -20x + 172

Multiply (-11 + x) * (-12 + x)
(-11(-12 + x) + x(-12 + x)) = -20x + 172
((-12 * -11 + x * -11) + x(-12 + x)) = -20x + 172
((132 + -11x) + x(-12 + x)) = -20x + 172
(132 + -11x + (-12 * x + x * x)) = -20x + 172
(132 + -11x + (-12x + x2)) = -20x + 172

Combine like terms: -11x + -12x = -23x
(132 + -23x + x2) = -20x + 172

Reorder the terms:
132 + -23x + x2 = 172 + -20x

Solving
132 + -23x + x2 = 172 + -20x

Solving for variable 'x'.

Reorder the terms:
132 + -172 + -23x + 20x + x2 = 172 + -20x + -172 + 20x

Combine like terms: 132 + -172 = -40
-40 + -23x + 20x + x2 = 172 + -20x + -172 + 20x

Combine like terms: -23x + 20x = -3x
-40 + -3x + x2 = 172 + -20x + -172 + 20x

Reorder the terms:
-40 + -3x + x2 = 172 + -172 + -20x + 20x

Combine like terms: 172 + -172 = 0
-40 + -3x + x2 = 0 + -20x + 20x
-40 + -3x + x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
-40 + -3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -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 '(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 = {-5, 8}

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