x(12-2x)(8-2x)=0e

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Solution for x(12-2x)(8-2x)=0e equation:


Simplifying
x(12 + -2x)(8 + -2x) = 0e

Multiply (12 + -2x) * (8 + -2x)
x(12(8 + -2x) + -2x * (8 + -2x)) = 0e
x((8 * 12 + -2x * 12) + -2x * (8 + -2x)) = 0e
x((96 + -24x) + -2x * (8 + -2x)) = 0e
x(96 + -24x + (8 * -2x + -2x * -2x)) = 0e
x(96 + -24x + (-16x + 4x2)) = 0e

Combine like terms: -24x + -16x = -40x
x(96 + -40x + 4x2) = 0e
(96 * x + -40x * x + 4x2 * x) = 0e
(96x + -40x2 + 4x3) = 0e

Anything times zero is zero.
96x + -40x2 + 4x3 = 0e

Solving
96x + -40x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(24 + -10x + x2) = 0

Factor a trinomial.
4x((4 + -1x)(6 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Subproblem 3

Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {0, 4, 6}

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