x(20-2x)(10-2x)=0

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Solution for x(20-2x)(10-2x)=0 equation: 


Simplifying
x(20 + -2x)(10 + -2x) = 0

Multiply (20 + -2x) * (10 + -2x)
x(20(10 + -2x) + -2x * (10 + -2x)) = 0
x((10 * 20 + -2x * 20) + -2x * (10 + -2x)) = 0
x((200 + -40x) + -2x * (10 + -2x)) = 0
x(200 + -40x + (10 * -2x + -2x * -2x)) = 0
x(200 + -40x + (-20x + 4x2)) = 0

Combine like terms: -40x + -20x = -60x
x(200 + -60x + 4x2) = 0
(200 * x + -60x * x + 4x2 * x) = 0
(200x + -60x2 + 4x3) = 0

Solving
200x + -60x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(50 + -15x + x2) = 0

Factor a trinomial.
4x((5 + -1x)(10 + -1x)) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5

Subproblem 3
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 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 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0, 5, 10}

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