((x^2)+x+5)+((x^2)+x-5)=0

Solution for ((x^2)+x+5)+((x^2)+x-5)=0 equation:

Simplifying
((x2) + x + 5) + ((x2) + x + -5) = 0
(x2 + x + 5) + ((x2) + x + -5) = 0

Reorder the terms:
(5 + x + x2) + ((x2) + x + -5) = 0

Remove parenthesis around (5 + x + x2)
5 + x + x2 + ((x2) + x + -5) = 0
5 + x + x2 + (x2 + x + -5) = 0

Reorder the terms:
5 + x + x2 + (-5 + x + x2) = 0

Remove parenthesis around (-5 + x + x2)
5 + x + x2 + -5 + x + x2 = 0

Reorder the terms:
5 + -5 + x + x + x2 + x2 = 0

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

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

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

Solving
2x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + x) = 0

Ignore the factor 2.
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}