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

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

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

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

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

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

Combine like terms: -5x + 5x = 0
5x(-25 + 0 + x2) = 0
5x(-25 + x2) = 0
(-25 * 5x + x2 * 5x) = 0
(-125x + 5x3) = 0

Solving
-125x + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(-25 + x2) = 0

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

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

Simplifying
5 + x = 0

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

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

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

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

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5
Solution
x = {0, -5, 5}