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

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


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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 2x + 2x = 4x
5 + 4x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2

Reorder the terms:
5 + 4x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
5 + 4x + -1x2 = 0 + -2x + 2x + x2 + -1x2
5 + 4x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
5 + 4x + -1x2 = 0 + x2 + -1x2
5 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
5 + 4x + -1x2 = 0

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {5, -1}

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