x^2-2x-1=3x+5

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Solution for x^2-2x-1=3x+5 equation: 


Simplifying
x2 + -2x + -1 = 3x + 5

Reorder the terms:
-1 + -2x + x2 = 3x + 5

Reorder the terms:
-1 + -2x + x2 = 5 + 3x

Solving
-1 + -2x + x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
-1 + -5 + -2x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -1 + -5 = -6
-6 + -2x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -2x + -3x = -5x
-6 + -5x + x2 = 5 + 3x + -5 + -3x

Reorder the terms:
-6 + -5x + x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
-6 + -5x + x2 = 0 + 3x + -3x
-6 + -5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-6 + -5x + x2 = 0

Factor a trinomial.
(-1 + -1x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

Simplifying
x = -1

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-1, 6}

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