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

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


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

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

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

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

Combine like terms: 6x + -2x = 4x
x(-12 + 4x + x2) = 0
(-12 * x + 4x * x + x2 * x) = 0
(-12x + 4x2 + x3) = 0

Solving
-12x + 4x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-12 + 4x + x2) = 0

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


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 '(-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

Subproblem 3
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
Solution
x = {0, -6, 2}

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