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

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


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

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

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

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

Combine like terms: 1x + 6x = 7x
(2 + 7x + 3x2) + -2 = 0

Reorder the terms:
2 + -2 + 7x + 3x2 = 0

Combine like terms: 2 + -2 = 0
0 + 7x + 3x2 = 0
7x + 3x2 = 0

Solving
7x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(7 + 3x) = 0


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 '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0, -2.333333333}

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