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

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

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

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

Solving for variable 'x'.

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

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

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

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

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

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

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

Factor a trinomial.
(-1 + -1x)(3 + -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 '(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

Solution

x = {-1, 3}
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