x^2(9x+5)(9x-5)=0

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Solution for x^2(9x+5)(9x-5)=0 equation: 


Simplifying
x2(9x + 5)(9x + -5) = 0

Reorder the terms:
x2(5 + 9x)(9x + -5) = 0

Reorder the terms:
x2(5 + 9x)(-5 + 9x) = 0

Multiply (5 + 9x) * (-5 + 9x)
x2(5(-5 + 9x) + 9x * (-5 + 9x)) = 0
x2((-5 * 5 + 9x * 5) + 9x * (-5 + 9x)) = 0
x2((-25 + 45x) + 9x * (-5 + 9x)) = 0
x2(-25 + 45x + (-5 * 9x + 9x * 9x)) = 0
x2(-25 + 45x + (-45x + 81x2)) = 0

Combine like terms: 45x + -45x = 0
x2(-25 + 0 + 81x2) = 0
x2(-25 + 81x2) = 0
(-25 * x2 + 81x2 * x2) = 0
(-25x2 + 81x4) = 0

Solving
-25x2 + 81x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-25 + 81x2) = 0

Factor a difference between two squares.
x2((5 + 9x)(-5 + 9x)) = 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 + 9x)' equal to zero and attempt to solve:

Simplifying
5 + 9x = 0

Solving
5 + 9x = 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 + 9x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 9x = 0 + -5
9x = 0 + -5

Combine like terms: 0 + -5 = -5
9x = -5

Divide each side by '9'.
x = -0.5555555556

Simplifying
x = -0.5555555556

Subproblem 3
Set the factor '(-5 + 9x)' equal to zero and attempt to solve:

Simplifying
-5 + 9x = 0

Solving
-5 + 9x = 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 + 9x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 9x = 0 + 5
9x = 0 + 5

Combine like terms: 0 + 5 = 5
9x = 5

Divide each side by '9'.
x = 0.5555555556

Simplifying
x = 0.5555555556
Solution
x = {0, -0.5555555556, 0.5555555556}

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