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

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


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

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

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

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

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

Solving
2x + 8x2 + 6x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(1 + 4x + 3x2) = 0

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

Ignore the factor 2.

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 + 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, -1, -0.3333333333}

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