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

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

Simplifying
(2 + 5x2)(2 + -5x2) = 0

Multiply (2 + 5x2) * (2 + -5x2)
(2(2 + -5x2) + 5x2 * (2 + -5x2)) = 0
((2 * 2 + -5x2 * 2) + 5x2 * (2 + -5x2)) = 0
((4 + -10x2) + 5x2 * (2 + -5x2)) = 0
(4 + -10x2 + (2 * 5x2 + -5x2 * 5x2)) = 0
(4 + -10x2 + (10x2 + -25x4)) = 0

Combine like terms: -10x2 + 10x2 = 0
(4 + 0 + -25x4) = 0
(4 + -25x4) = 0

Solving
4 + -25x4 = 0

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + -25x4 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -25x4 = 0 + -4
-25x4 = 0 + -4

Combine like terms: 0 + -4 = -4
-25x4 = -4

Divide each side by '-25'.
x4 = 0.16

Simplifying
x4 = 0.16

Reorder the terms:
-0.16 + x4 = 0.16 + -0.16

Combine like terms: 0.16 + -0.16 = 0.00
-0.16 + x4 = 0.00

Factor a difference between two squares.
(0.4 + x2)(-0.4 + x2) = 0.00

Subproblem 1
Set the factor '(0.4 + x2)' equal to zero and attempt to solve:

Simplifying
0.4 + x2 = 0

Solving
0.4 + x2 = 0

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + x2 = 0 + -0.4
x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
x2 = -0.4

Simplifying
x2 = -0.4

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(-0.4 + x2)' equal to zero and attempt to solve:

Simplifying
-0.4 + x2 = 0

Solving
-0.4 + x2 = 0

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x2 = 0 + 0.4
x2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
x2 = 0.4

Simplifying
x2 = 0.4

Take the square root of each side:
x = {-0.632455532, 0.632455532}
Solution
x = {-0.632455532, 0.632455532}