0=9x^4-25x^2

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Solution for 0=9x^4-25x^2 equation: 


Simplifying
0 = 9x4 + -25x2

Reorder the terms:
0 = -25x2 + 9x4

Solving
0 = -25x2 + 9x4

Solving for variable 'x'.
Remove the zero:
25x2 + -9x4 = -25x2 + 9x4 + 25x2 + -9x4

Reorder the terms:
25x2 + -9x4 = -25x2 + 25x2 + 9x4 + -9x4

Combine like terms: -25x2 + 25x2 = 0
25x2 + -9x4 = 0 + 9x4 + -9x4
25x2 + -9x4 = 9x4 + -9x4

Combine like terms: 9x4 + -9x4 = 0
25x2 + -9x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(25 + -9x2) = 0

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


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 '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667

Subproblem 3
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667
Solution
x = {0, -1.666666667, 1.666666667}

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