(x-11)(x-12)=-19x+164

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Solution for (x-11)(x-12)=-19x+164 equation: 


Simplifying
(x + -11)(x + -12) = -19x + 164

Reorder the terms:
(-11 + x)(x + -12) = -19x + 164

Reorder the terms:
(-11 + x)(-12 + x) = -19x + 164

Multiply (-11 + x) * (-12 + x)
(-11(-12 + x) + x(-12 + x)) = -19x + 164
((-12 * -11 + x * -11) + x(-12 + x)) = -19x + 164
((132 + -11x) + x(-12 + x)) = -19x + 164
(132 + -11x + (-12 * x + x * x)) = -19x + 164
(132 + -11x + (-12x + x2)) = -19x + 164

Combine like terms: -11x + -12x = -23x
(132 + -23x + x2) = -19x + 164

Reorder the terms:
132 + -23x + x2 = 164 + -19x

Solving
132 + -23x + x2 = 164 + -19x

Solving for variable 'x'.

Reorder the terms:
132 + -164 + -23x + 19x + x2 = 164 + -19x + -164 + 19x

Combine like terms: 132 + -164 = -32
-32 + -23x + 19x + x2 = 164 + -19x + -164 + 19x

Combine like terms: -23x + 19x = -4x
-32 + -4x + x2 = 164 + -19x + -164 + 19x

Reorder the terms:
-32 + -4x + x2 = 164 + -164 + -19x + 19x

Combine like terms: 164 + -164 = 0
-32 + -4x + x2 = 0 + -19x + 19x
-32 + -4x + x2 = -19x + 19x

Combine like terms: -19x + 19x = 0
-32 + -4x + x2 = 0

Factor a trinomial.
(-4 + -1x)(8 + -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 '(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 = {-4, 8}

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