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

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


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

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

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

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

Combine like terms: 1x + 2x = 3x
3x(1 + 3x + 2x2) = 0
(1 * 3x + 3x * 3x + 2x2 * 3x) = 0
(3x + 9x2 + 6x3) = 0

Solving
3x + 9x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 3x + 2x2) = 0

Factor a trinomial.
3x((1 + x)(1 + 2x)) = 0

Ignore the factor 3.

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1

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, -1, -0.5}

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