5x(x-6)(x-2)=0

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Solution for 5x(x-6)(x-2)=0 equation:


Simplifying
5x(x + -6)(x + -2) = 0

Reorder the terms:
5x(-6 + x)(x + -2) = 0

Reorder the terms:
5x(-6 + x)(-2 + x) = 0

Multiply (-6 + x) * (-2 + x)
5x(-6(-2 + x) + x(-2 + x)) = 0
5x((-2 * -6 + x * -6) + x(-2 + x)) = 0
5x((12 + -6x) + x(-2 + x)) = 0
5x(12 + -6x + (-2 * x + x * x)) = 0
5x(12 + -6x + (-2x + x2)) = 0

Combine like terms: -6x + -2x = -8x
5x(12 + -8x + x2) = 0
(12 * 5x + -8x * 5x + x2 * 5x) = 0
(60x + -40x2 + 5x3) = 0

Solving
60x + -40x2 + 5x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5x'.
5x(12 + -8x + x2) = 0

Factor a trinomial.
5x((2 + -1x)(6 + -1x)) = 0

Ignore the factor 5.

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 '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

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, 2, 6}

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