45x^2-80x^6=

Solution for 45x^2-80x^6= equation:

Simplifying
45x2 + -80x6 = 0

Solving
45x2 + -80x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(9 + -16x4) = 0

Factor a difference between two squares.
5x2((3 + 4x2)(3 + -4x2)) = 0

Ignore the factor 5.
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 '(3 + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 4x2 = 0

Solving
3 + 4x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + 4x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4x2 = 0 + -3
4x2 = 0 + -3

Combine like terms: 0 + -3 = -3
4x2 = -3

Divide each side by '4'.
x2 = -0.75

Simplifying
x2 = -0.75

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(3 + -4x2)' equal to zero and attempt to solve:

Simplifying
3 + -4x2 = 0

Solving
3 + -4x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x2 = 0 + -3
-4x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-4x2 = -3

Divide each side by '-4'.
x2 = 0.75

Simplifying
x2 = 0.75

Take the square root of each side:
x = {-0.866025404, 0.866025404}
Solution
x = {0, -0.866025404, 0.866025404}