x(2x-10)(2x+10)=0

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Solution for x(2x-10)(2x+10)=0 equation: 


Simplifying
x(2x + -10)(2x + 10) = 0

Reorder the terms:
x(-10 + 2x)(2x + 10) = 0

Reorder the terms:
x(-10 + 2x)(10 + 2x) = 0

Multiply (-10 + 2x) * (10 + 2x)
x(-10(10 + 2x) + 2x * (10 + 2x)) = 0
x((10 * -10 + 2x * -10) + 2x * (10 + 2x)) = 0
x((-100 + -20x) + 2x * (10 + 2x)) = 0
x(-100 + -20x + (10 * 2x + 2x * 2x)) = 0
x(-100 + -20x + (20x + 4x2)) = 0

Combine like terms: -20x + 20x = 0
x(-100 + 0 + 4x2) = 0
x(-100 + 4x2) = 0
(-100 * x + 4x2 * x) = 0
(-100x + 4x3) = 0

Solving
-100x + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-25 + x2) = 0

Factor a difference between two squares.
4x((5 + x)(-5 + x)) = 0

Ignore the factor 4.

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}

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