Simplifying
x + 2 = 3x + -1x^{2} + 5
Reorder the terms:
2 + x = 3x + -1x^{2} + 5
Reorder the terms:
2 + x = 5 + 3x + -1x^{2}
Solving
2 + x = 5 + 3x + -1x^{2}
Solving for variable 'x'.
Reorder the terms:
2 + -5 + x + -3x + x^{2} = 5 + 3x + -1x^{2} + -5 + -3x + x^{2}
Combine like terms: 2 + -5 = -3
-3 + x + -3x + x^{2} = 5 + 3x + -1x^{2} + -5 + -3x + x^{2}
Combine like terms: x + -3x = -2x
-3 + -2x + x^{2} = 5 + 3x + -1x^{2} + -5 + -3x + x^{2}
Reorder the terms:
-3 + -2x + x^{2} = 5 + -5 + 3x + -3x + -1x^{2} + x^{2}
Combine like terms: 5 + -5 = 0
-3 + -2x + x^{2} = 0 + 3x + -3x + -1x^{2} + x^{2}
-3 + -2x + x^{2} = 3x + -3x + -1x^{2} + x^{2}
Combine like terms: 3x + -3x = 0
-3 + -2x + x^{2} = 0 + -1x^{2} + x^{2}
-3 + -2x + x^{2} = -1x^{2} + x^{2}
Combine like terms: -1x^{2} + x^{2} = 0
-3 + -2x + x^{2} = 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}