4x(3x+1)(2x+1)=0

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Solution for 4x(3x+1)(2x+1)=0 equation: 


Simplifying
4x(3x + 1)(2x + 1) = 0

Reorder the terms:
4x(1 + 3x)(2x + 1) = 0

Reorder the terms:
4x(1 + 3x)(1 + 2x) = 0

Multiply (1 + 3x) * (1 + 2x)
4x(1(1 + 2x) + 3x * (1 + 2x)) = 0
4x((1 * 1 + 2x * 1) + 3x * (1 + 2x)) = 0
4x((1 + 2x) + 3x * (1 + 2x)) = 0
4x(1 + 2x + (1 * 3x + 2x * 3x)) = 0
4x(1 + 2x + (3x + 6x2)) = 0

Combine like terms: 2x + 3x = 5x
4x(1 + 5x + 6x2) = 0
(1 * 4x + 5x * 4x + 6x2 * 4x) = 0
(4x + 20x2 + 24x3) = 0

Solving
4x + 20x2 + 24x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4x'.
4x(1 + 5x + 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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