(2x^2-5)(2x^2+5)=75

Solution for (2x^2-5)(2x^2+5)=75 equation:

Simplifying
(2x2 + -5)(2x2 + 5) = 75

Reorder the terms:
(-5 + 2x2)(2x2 + 5) = 75

Reorder the terms:
(-5 + 2x2)(5 + 2x2) = 75

Multiply (-5 + 2x2) * (5 + 2x2)
(-5(5 + 2x2) + 2x2 * (5 + 2x2)) = 75
((5 * -5 + 2x2 * -5) + 2x2 * (5 + 2x2)) = 75
((-25 + -10x2) + 2x2 * (5 + 2x2)) = 75
(-25 + -10x2 + (5 * 2x2 + 2x2 * 2x2)) = 75
(-25 + -10x2 + (10x2 + 4x4)) = 75

Combine like terms: -10x2 + 10x2 = 0
(-25 + 0 + 4x4) = 75
(-25 + 4x4) = 75

Solving
-25 + 4x4 = 75

Solving for variable 'x'.

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

Add '25' to each side of the equation.
-25 + 25 + 4x4 = 75 + 25

Combine like terms: -25 + 25 = 0
0 + 4x4 = 75 + 25
4x4 = 75 + 25

Combine like terms: 75 + 25 = 100
4x4 = 100

Divide each side by '4'.
x4 = 25

Simplifying
x4 = 25

Reorder the terms:
-25 + x4 = 25 + -25

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

Factor a difference between two squares.
(5 + x2)(-5 + x2) = 0

Subproblem 1
Set the factor '(5 + x2)' equal to zero and attempt to solve:

Simplifying
5 + x2 = 0

Solving
5 + x2 = 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 + x2 = 0 + -5

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

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

Simplifying
x2 = -5

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 '(-5 + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x2 = 0

Solving
-5 + x2 = 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 + x2 = 0 + 5

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

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

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-2.236067978, 2.236067978}