3-x=x^2+1

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

Simplifying
3 + -1x = x2 + 1

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

Solving
3 + -1x = 1 + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(1 + -1x)(2 + x) = 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 '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {1, -2}