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

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


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

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

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

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

Combine like terms: 2x + -3x = -1x
(-2 + -1x + 3x2) + (3x + 2)(x + 1) = 0

Reorder the terms:
-2 + -1x + 3x2 + (2 + 3x)(x + 1) = 0

Reorder the terms:
-2 + -1x + 3x2 + (2 + 3x)(1 + x) = 0

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

Combine like terms: 2x + 3x = 5x
-2 + -1x + 3x2 + (2 + 5x + 3x2) = 0

Reorder the terms:
-2 + 2 + -1x + 5x + 3x2 + 3x2 = 0

Combine like terms: -2 + 2 = 0
0 + -1x + 5x + 3x2 + 3x2 = 0
-1x + 5x + 3x2 + 3x2 = 0

Combine like terms: -1x + 5x = 4x
4x + 3x2 + 3x2 = 0

Combine like terms: 3x2 + 3x2 = 6x2
4x + 6x2 = 0

Solving
4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}

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