x^2+1=3-x

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

Simplifying
x2 + 1 = 3 + -1x

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

Solving
1 + x2 = 3 + -1x

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(-2 + -1x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve:

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

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