0=(5x^4)-(45x^2)

Solution for 0=(5x^4)-(45x^2) equation:

Simplifying
0 = (5x4) + -1(45x2)

Remove parenthesis around (45x2)
0 = (5x4) + -1 * 45x2

Multiply -1 * 45
0 = (5x4) + -45x2

Reorder the terms:
0 = -45x2 + (5x4)

Solving
0 = -45x2 + (5x4)

Solving for variable 'x'.
Remove the zero:
45x2 + (-5x4) = -45x2 + (5x4) + 45x2 + (-5x4)

Reorder the terms:
45x2 + (-5x4) = -45x2 + 45x2 + (5x4) + (-5x4)

Combine like terms: -45x2 + 45x2 = 0
45x2 + (-5x4) = 0 + (5x4) + (-5x4)
45x2 + (-5x4) = (5x4) + (-5x4)

Combine like terms: (5x4) + (-5x4) = 0
45x2 + (-5x4) = 0

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(9 + (-1x2)) = 0

Factor a difference between two squares.
5x2((3 + x)(3 + (-1x))) = 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 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 3
Set the factor '(3 + (-1x))' equal to zero and attempt to solve:

Simplifying
3 + (-1x) = 0

Solving
3 + (-1x) = 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 + (-1x) = 0 + -3

Combine like terms: 3 + -3 = 0
0 + (-1x) = 0 + -3
(-1x) = 0 + -3

Combine like terms: 0 + -3 = -3
(-1x) = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}