x^2-x-5=-3x-2

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


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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
(-3 + -1x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

Subproblem 2
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
Solution
x = {-3, 1}

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