(x^2+x-1)(x^2-x-1)=0

Solution for (x^2+x-1)(x^2-x-1)=0 equation:

Simplifying
(x2 + x + -1)(x2 + -1x + -1) = 0

Reorder the terms:
(-1 + x + x2)(x2 + -1x + -1) = 0

Reorder the terms:
(-1 + x + x2)(-1 + -1x + x2) = 0

Multiply (-1 + x + x2) * (-1 + -1x + x2)
(-1(-1 + -1x + x2) + x(-1 + -1x + x2) + x2(-1 + -1x + x2)) = 0
((-1 * -1 + -1x * -1 + x2 * -1) + x(-1 + -1x + x2) + x2(-1 + -1x + x2)) = 0
((1 + 1x + -1x2) + x(-1 + -1x + x2) + x2(-1 + -1x + x2)) = 0
(1 + 1x + -1x2 + (-1 * x + -1x * x + x2 * x) + x2(-1 + -1x + x2)) = 0
(1 + 1x + -1x2 + (-1x + -1x2 + x3) + x2(-1 + -1x + x2)) = 0
(1 + 1x + -1x2 + -1x + -1x2 + x3 + (-1 * x2 + -1x * x2 + x2 * x2)) = 0
(1 + 1x + -1x2 + -1x + -1x2 + x3 + (-1x2 + -1x3 + x4)) = 0

Reorder the terms:
(1 + 1x + -1x + -1x2 + -1x2 + -1x2 + x3 + -1x3 + x4) = 0

Combine like terms: 1x + -1x = 0
(1 + 0 + -1x2 + -1x2 + -1x2 + x3 + -1x3 + x4) = 0
(1 + -1x2 + -1x2 + -1x2 + x3 + -1x3 + x4) = 0

Combine like terms: -1x2 + -1x2 = -2x2
(1 + -2x2 + -1x2 + x3 + -1x3 + x4) = 0

Combine like terms: -2x2 + -1x2 = -3x2
(1 + -3x2 + x3 + -1x3 + x4) = 0

Combine like terms: x3 + -1x3 = 0
(1 + -3x2 + 0 + x4) = 0
(1 + -3x2 + x4) = 0

Solving
1 + -3x2 + x4 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3x2 + -1 + x4 = 0 + -1

Reorder the terms:
1 + -1 + -3x2 + x4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x2 + x4 = 0 + -1
-3x2 + x4 = 0 + -1

Combine like terms: 0 + -1 = -1
-3x2 + x4 = -1

The x term is -3x2.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x2 + 2.25 + x4 = -1 + 2.25

Reorder the terms:
2.25 + -3x2 + x4 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3x2 + x4 = 1.25

Factor a perfect square on the left side:
(x2 + -1.5)(x2 + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x2 + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x2 + -1.5 = 1.118033989

Simplifying
x2 + -1.5 = 1.118033989

Reorder the terms:
-1.5 + x2 = 1.118033989

Solving
-1.5 + x2 = 1.118033989

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = 1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = 1.118033989 + 1.5
x2 = 1.118033989 + 1.5

Combine like terms: 1.118033989 + 1.5 = 2.618033989
x2 = 2.618033989

Simplifying
x2 = 2.618033989

Take the square root of each side:
x = {-1.618033989, 1.618033989}

Subproblem 2
x2 + -1.5 = -1.118033989

Simplifying
x2 + -1.5 = -1.118033989

Reorder the terms:
-1.5 + x2 = -1.118033989

Solving
-1.5 + x2 = -1.118033989

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x2 = -1.118033989 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x2 = -1.118033989 + 1.5
x2 = -1.118033989 + 1.5

Combine like terms: -1.118033989 + 1.5 = 0.381966011
x2 = 0.381966011

Simplifying
x2 = 0.381966011

Take the square root of each side:
x = {-0.618033989, 0.618033989}

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.618033989, 1.618033989, -0.618033989, 0.618033989}