(x^2-5)(x^2+4)=-20

Solution for (x^2-5)(x^2+4)=-20 equation:

Simplifying
(x2 + -5)(x2 + 4) = -20

Reorder the terms:
(-5 + x2)(x2 + 4) = -20

Reorder the terms:
(-5 + x2)(4 + x2) = -20

Multiply (-5 + x2) * (4 + x2)
(-5(4 + x2) + x2(4 + x2)) = -20
((4 * -5 + x2 * -5) + x2(4 + x2)) = -20
((-20 + -5x2) + x2(4 + x2)) = -20
(-20 + -5x2 + (4 * x2 + x2 * x2)) = -20
(-20 + -5x2 + (4x2 + x4)) = -20

Combine like terms: -5x2 + 4x2 = -1x2
(-20 + -1x2 + x4) = -20

Add '20' to each side of the equation.
-20 + -1x2 + 20 + x4 = -20 + 20

Reorder the terms:
-20 + 20 + -1x2 + x4 = -20 + 20

Combine like terms: -20 + 20 = 0
0 + -1x2 + x4 = -20 + 20
-1x2 + x4 = -20 + 20

Combine like terms: -20 + 20 = 0
-1x2 + x4 = 0

Solving
-1x2 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-1 + x2) = 0

Factor a difference between two squares.
x2((1 + x)(-1 + x)) = 0

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
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
Subproblem 3
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, 1}