(x-1)(x-1)=2x^2-x-19

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Solution for (x-1)(x-1)=2x^2-x-19 equation: 


Simplifying
(x + -1)(x + -1) = 2x2 + -1x + -19

Reorder the terms:
(-1 + x)(x + -1) = 2x2 + -1x + -19

Reorder the terms:
(-1 + x)(-1 + x) = 2x2 + -1x + -19

Multiply (-1 + x) * (-1 + x)
(-1(-1 + x) + x(-1 + x)) = 2x2 + -1x + -19
((-1 * -1 + x * -1) + x(-1 + x)) = 2x2 + -1x + -19
((1 + -1x) + x(-1 + x)) = 2x2 + -1x + -19
(1 + -1x + (-1 * x + x * x)) = 2x2 + -1x + -19
(1 + -1x + (-1x + x2)) = 2x2 + -1x + -19

Combine like terms: -1x + -1x = -2x
(1 + -2x + x2) = 2x2 + -1x + -19

Reorder the terms:
1 + -2x + x2 = -19 + -1x + 2x2

Solving
1 + -2x + x2 = -19 + -1x + 2x2

Solving for variable 'x'.

Reorder the terms:
1 + 19 + -2x + x + x2 + -2x2 = -19 + -1x + 2x2 + 19 + x + -2x2

Combine like terms: 1 + 19 = 20
20 + -2x + x + x2 + -2x2 = -19 + -1x + 2x2 + 19 + x + -2x2

Combine like terms: -2x + x = -1x
20 + -1x + x2 + -2x2 = -19 + -1x + 2x2 + 19 + x + -2x2

Combine like terms: x2 + -2x2 = -1x2
20 + -1x + -1x2 = -19 + -1x + 2x2 + 19 + x + -2x2

Reorder the terms:
20 + -1x + -1x2 = -19 + 19 + -1x + x + 2x2 + -2x2

Combine like terms: -19 + 19 = 0
20 + -1x + -1x2 = 0 + -1x + x + 2x2 + -2x2
20 + -1x + -1x2 = -1x + x + 2x2 + -2x2

Combine like terms: -1x + x = 0
20 + -1x + -1x2 = 0 + 2x2 + -2x2
20 + -1x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
20 + -1x + -1x2 = 0

Factor a trinomial.
(4 + -1x)(5 + x) = 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 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 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {4, -5}

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