13-x=x^2+1

Solution for 13-x=x^2+1 equation:

Simplifying
13 + -1x = x2 + 1

Reorder the terms:
13 + -1x = 1 + x2

Solving
13 + -1x = 1 + x2

Solving for variable 'x'.

Reorder the terms:
13 + -1 + -1x + -1x2 = 1 + x2 + -1 + -1x2

Combine like terms: 13 + -1 = 12
12 + -1x + -1x2 = 1 + x2 + -1 + -1x2

Reorder the terms:
12 + -1x + -1x2 = 1 + -1 + x2 + -1x2

Combine like terms: 1 + -1 = 0
12 + -1x + -1x2 = 0 + x2 + -1x2
12 + -1x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -1x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(4 + x) = 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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {3, -4}