x^2-5+x+6=1

Solution for x^2-5+x+6=1 equation:

Simplifying
x2 + -5 + x + 6 = 1

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

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

Add '-1' to each side of the equation.
1 + x + -1 + x2 = 1 + -1

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

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

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

Solving
x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

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

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

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

Simplifying
x = -1
Solution
x = {0, -1}