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

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


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

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

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

Reorder the terms for easier multiplication:
-3x(1 + 2x)(2 + 4x) = 0

Multiply (1 + 2x) * (2 + 4x)
-3x(1(2 + 4x) + 2x * (2 + 4x)) = 0
-3x((2 * 1 + 4x * 1) + 2x * (2 + 4x)) = 0
-3x((2 + 4x) + 2x * (2 + 4x)) = 0
-3x(2 + 4x + (2 * 2x + 4x * 2x)) = 0
-3x(2 + 4x + (4x + 8x2)) = 0

Combine like terms: 4x + 4x = 8x
-3x(2 + 8x + 8x2) = 0
(2 * -3x + 8x * -3x + 8x2 * -3x) = 0
(-6x + -24x2 + -24x3) = 0

Solving
-6x + -24x2 + -24x3 = 0

Solving for variable 'x'.

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

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

Ignore the factor -6.

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 + 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, -0.5, -0.5}

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