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

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

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

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

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

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

Solving for variable 'x'.

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

Combine like terms: -1 + -3 = -4
-4 + -1x + -2x + x2 = 3 + 2x + -3 + -2x

Combine like terms: -1x + -2x = -3x
-4 + -3x + x2 = 3 + 2x + -3 + -2x

Reorder the terms:
-4 + -3x + x2 = 3 + -3 + 2x + -2x

Combine like terms: 3 + -3 = 0
-4 + -3x + x2 = 0 + 2x + -2x
-4 + -3x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-4 + -3x + x2 = 0

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