2x(4x+2)(3x+6)=0

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Solution for 2x(4x+2)(3x+6)=0 equation: 


Simplifying
2x(4x + 2)(3x + 6) = 0

Reorder the terms:
2x(2 + 4x)(3x + 6) = 0

Reorder the terms:
2x(2 + 4x)(6 + 3x) = 0

Multiply (2 + 4x) * (6 + 3x)
2x(2(6 + 3x) + 4x * (6 + 3x)) = 0
2x((6 * 2 + 3x * 2) + 4x * (6 + 3x)) = 0
2x((12 + 6x) + 4x * (6 + 3x)) = 0
2x(12 + 6x + (6 * 4x + 3x * 4x)) = 0
2x(12 + 6x + (24x + 12x2)) = 0

Combine like terms: 6x + 24x = 30x
2x(12 + 30x + 12x2) = 0
(12 * 2x + 30x * 2x + 12x2 * 2x) = 0
(24x + 60x2 + 24x3) = 0

Solving
24x + 60x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(2 + 5x + 2x2) = 0

Factor a trinomial.
12x((2 + x)(1 + 2x)) = 0

Ignore the factor 12.

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 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

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

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

Simplifying
x = -2

Subproblem 3
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
Solution
x = {0, -2, -0.5}

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