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

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


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

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

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

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

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

Reorder the terms:
2 + 5x + -3x2 + 2(1 + 3x) = 0
2 + 5x + -3x2 + (1 * 2 + 3x * 2) = 0
2 + 5x + -3x2 + (2 + 6x) = 0

Reorder the terms:
2 + 2 + 5x + 6x + -3x2 = 0

Combine like terms: 2 + 2 = 4
4 + 5x + 6x + -3x2 = 0

Combine like terms: 5x + 6x = 11x
4 + 11x + -3x2 = 0

Solving
4 + 11x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -1x)(1 + 3x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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 = {4, -0.3333333333}

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