x^2-2x-1=x+39

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Solution for x^2-2x-1=x+39 equation: 


Simplifying
x2 + -2x + -1 = x + 39

Reorder the terms:
-1 + -2x + x2 = x + 39

Reorder the terms:
-1 + -2x + x2 = 39 + x

Solving
-1 + -2x + x2 = 39 + x

Solving for variable 'x'.

Reorder the terms:
-1 + -39 + -2x + -1x + x2 = 39 + x + -39 + -1x

Combine like terms: -1 + -39 = -40
-40 + -2x + -1x + x2 = 39 + x + -39 + -1x

Combine like terms: -2x + -1x = -3x
-40 + -3x + x2 = 39 + x + -39 + -1x

Reorder the terms:
-40 + -3x + x2 = 39 + -39 + x + -1x

Combine like terms: 39 + -39 = 0
-40 + -3x + x2 = 0 + x + -1x
-40 + -3x + x2 = x + -1x

Combine like terms: x + -1x = 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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