(5x-3)x(5x+3)=0

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Solution for (5x-3)x(5x+3)=0 equation: 


Simplifying
(5x + -3) * x(5x + 3) = 0

Reorder the terms:
(-3 + 5x) * x(5x + 3) = 0

Reorder the terms:
(-3 + 5x) * x(3 + 5x) = 0

Reorder the terms for easier multiplication:
x(-3 + 5x)(3 + 5x) = 0

Multiply (-3 + 5x) * (3 + 5x)
x(-3(3 + 5x) + 5x * (3 + 5x)) = 0
x((3 * -3 + 5x * -3) + 5x * (3 + 5x)) = 0
x((-9 + -15x) + 5x * (3 + 5x)) = 0
x(-9 + -15x + (3 * 5x + 5x * 5x)) = 0
x(-9 + -15x + (15x + 25x2)) = 0

Combine like terms: -15x + 15x = 0
x(-9 + 0 + 25x2) = 0
x(-9 + 25x2) = 0
(-9 * x + 25x2 * x) = 0
(-9x + 25x3) = 0

Solving
-9x + 25x3 = 0

Solving for variable 'x'.

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

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


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(3 + 5x)' equal to zero and attempt to solve:

Simplifying
3 + 5x = 0

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

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

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

Divide each side by '5'.
x = -0.6

Simplifying
x = -0.6

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

Simplifying
-3 + 5x = 0

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

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

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

Divide each side by '5'.
x = 0.6

Simplifying
x = 0.6
Solution
x = {0, -0.6, 0.6}

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