-x^2+1=5x+1

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


Simplifying
-1x2 + 1 = 5x + 1

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

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

Add '-1' to each side of the equation.
1 + -1 + -1x2 = 1 + -1 + 5x

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

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

Solving
-1x2 = 5x

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '-1x'.
-1x(5 + x) = 0

Ignore the factor -1.

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {0, -5}

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