(x-1)(2x-2)=162

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Solution for (x-1)(2x-2)=162 equation: 


Simplifying
(x + -1)(2x + -2) = 162

Reorder the terms:
(-1 + x)(2x + -2) = 162

Reorder the terms:
(-1 + x)(-2 + 2x) = 162

Multiply (-1 + x) * (-2 + 2x)
(-1(-2 + 2x) + x(-2 + 2x)) = 162
((-2 * -1 + 2x * -1) + x(-2 + 2x)) = 162
((2 + -2x) + x(-2 + 2x)) = 162
(2 + -2x + (-2 * x + 2x * x)) = 162
(2 + -2x + (-2x + 2x2)) = 162

Combine like terms: -2x + -2x = -4x
(2 + -4x + 2x2) = 162

Solving
2 + -4x + 2x2 = 162

Solving for variable 'x'.

Reorder the terms:
2 + -162 + -4x + 2x2 = 162 + -162

Combine like terms: 2 + -162 = -160
-160 + -4x + 2x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-160 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + -2x + x2) = 0

Factor a trinomial.
2((-8 + -1x)(10 + -1x)) = 0

Ignore the factor 2.

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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-8, 10}

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