25x^4-40x^2+16=0

Solution for 25x^4-40x^2+16=0 equation:

Simplifying
25x4 + -40x2 + 16 = 0

Reorder the terms:
16 + -40x2 + 25x4 = 0

Solving
16 + -40x2 + 25x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -5x2)(4 + -5x2) = 0

Subproblem 1
Set the factor '(4 + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x2 = 0

Solving
4 + -5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x2 = 0 + -4
-5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}
Subproblem 2
Set the factor '(4 + -5x2)' equal to zero and attempt to solve:

Simplifying
4 + -5x2 = 0

Solving
4 + -5x2 = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x2 = 0 + -4
-5x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-5x2 = -4

Divide each side by '-5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}
Solution
x = {-0.894427191, 0.894427191, -0.894427191, 0.894427191}