(x)(10-2x)(6-2x)=0

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Solution for (x)(10-2x)(6-2x)=0 equation:


Simplifying
(x)(10 + -2x)(6 + -2x) = 0

Multiply (10 + -2x) * (6 + -2x)
x(10(6 + -2x) + -2x * (6 + -2x)) = 0
x((6 * 10 + -2x * 10) + -2x * (6 + -2x)) = 0
x((60 + -20x) + -2x * (6 + -2x)) = 0
x(60 + -20x + (6 * -2x + -2x * -2x)) = 0
x(60 + -20x + (-12x + 4x2)) = 0

Combine like terms: -20x + -12x = -32x
x(60 + -32x + 4x2) = 0
(60 * x + -32x * x + 4x2 * x) = 0
(60x + -32x2 + 4x3) = 0

Solving
60x + -32x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(15 + -8x + x2) = 0

Factor a trinomial.
4x((3 + -1x)(5 + -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 '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 3

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

Solution

x = {0, 3, 5}

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