5x-1=3x+2-x^2

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Solution for 5x-1=3x+2-x^2 equation: 


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

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

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

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

Solving for variable 'x'.

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

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

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

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

Combine like terms: 2 + -2 = 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.
(-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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