-x^2+1=x-5

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

Simplifying
-1x2 + 1 = x + -5

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

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

Solving
1 + -1x2 = -5 + x

Solving for variable 'x'.

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

Combine like terms: 1 + 5 = 6
6 + -1x + -1x2 = -5 + x + 5 + -1x

Reorder the terms:
6 + -1x + -1x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
6 + -1x + -1x2 = 0 + x + -1x
6 + -1x + -1x2 = x + -1x

Combine like terms: x + -1x = 0
6 + -1x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(3 + x) = 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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {2, -3}