(x-10)(x+10)(x)=0

Solution for (x-10)(x+10)(x)=0 equation:

Simplifying
(x + -10)(x + 10)(x) = 0

Reorder the terms:
(-10 + x)(x + 10)(x) = 0

Reorder the terms:
(-10 + x)(10 + x)(x) = 0

Reorder the terms for easier multiplication:
x(-10 + x)(10 + x) = 0

Multiply (-10 + x) * (10 + x)
x(-10(10 + x) + x(10 + x)) = 0
x((10 * -10 + x * -10) + x(10 + x)) = 0
x((-100 + -10x) + x(10 + x)) = 0
x(-100 + -10x + (10 * x + x * x)) = 0
x(-100 + -10x + (10x + x2)) = 0

Combine like terms: -10x + 10x = 0
x(-100 + 0 + x2) = 0
x(-100 + x2) = 0
(-100 * x + x2 * x) = 0
(-100x + x3) = 0

Solving
-100x + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-100 + x2) = 0

Factor a difference between two squares.
x((10 + x)(-10 + x)) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 0

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

Add '-10' to each side of the equation.
10 + -10 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Subproblem 3
Set the factor '(-10 + x)' equal to zero and attempt to solve:

Simplifying
-10 + x = 0

Solving
-10 + x = 0

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

Add '10' to each side of the equation.
-10 + 10 + x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + x = 0 + 10
x = 0 + 10

Combine like terms: 0 + 10 = 10
x = 10

Simplifying
x = 10
Solution
x = {0, -10, 10}