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

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


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

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

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

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

Combine like terms: -1x + 6x = 5x
(2 + 5x + -3x2) + 2(3x + 1)(2x + -1) = 0

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

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

Multiply (1 + 3x) * (-1 + 2x)
2 + 5x + -3x2 + 2(1(-1 + 2x) + 3x * (-1 + 2x)) = 0
2 + 5x + -3x2 + 2((-1 * 1 + 2x * 1) + 3x * (-1 + 2x)) = 0
2 + 5x + -3x2 + 2((-1 + 2x) + 3x * (-1 + 2x)) = 0
2 + 5x + -3x2 + 2(-1 + 2x + (-1 * 3x + 2x * 3x)) = 0
2 + 5x + -3x2 + 2(-1 + 2x + (-3x + 6x2)) = 0

Combine like terms: 2x + -3x = -1x
2 + 5x + -3x2 + 2(-1 + -1x + 6x2) = 0
2 + 5x + -3x2 + (-1 * 2 + -1x * 2 + 6x2 * 2) = 0
2 + 5x + -3x2 + (-2 + -2x + 12x2) = 0

Reorder the terms:
2 + -2 + 5x + -2x + -3x2 + 12x2 = 0

Combine like terms: 2 + -2 = 0
0 + 5x + -2x + -3x2 + 12x2 = 0
5x + -2x + -3x2 + 12x2 = 0

Combine like terms: 5x + -2x = 3x
3x + -3x2 + 12x2 = 0

Combine like terms: -3x2 + 12x2 = 9x2
3x + 9x2 = 0

Solving
3x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(1 + 3x) = 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 + 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, -0.3333333333}

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