(4x+2)x(6x-2)=0

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Solution for (4x+2)x(6x-2)=0 equation: 


Simplifying
(4x + 2) * x(6x + -2) = 0

Reorder the terms:
(2 + 4x) * x(6x + -2) = 0

Reorder the terms:
(2 + 4x) * x(-2 + 6x) = 0

Reorder the terms for easier multiplication:
x(2 + 4x)(-2 + 6x) = 0

Multiply (2 + 4x) * (-2 + 6x)
x(2(-2 + 6x) + 4x * (-2 + 6x)) = 0
x((-2 * 2 + 6x * 2) + 4x * (-2 + 6x)) = 0
x((-4 + 12x) + 4x * (-2 + 6x)) = 0
x(-4 + 12x + (-2 * 4x + 6x * 4x)) = 0
x(-4 + 12x + (-8x + 24x2)) = 0

Combine like terms: 12x + -8x = 4x
x(-4 + 4x + 24x2) = 0
(-4 * x + 4x * x + 24x2 * x) = 0
(-4x + 4x2 + 24x3) = 0

Solving
-4x + 4x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-1 + x + 6x2) = 0

Factor a trinomial.
4x((-1 + -2x)(1 + -3x)) = 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 '(-1 + -2x)' equal to zero and attempt to solve:

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -2x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2x = 0 + 1
-2x = 0 + 1

Combine like terms: 0 + 1 = 1
-2x = 1

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {0, -0.5, 0.3333333333}

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