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

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


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

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

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

Combine like terms: 6x + 3x = 9x
9x + 3x2 = 2x + -2

Reorder the terms:
9x + 3x2 = -2 + 2x

Solving
9x + 3x2 = -2 + 2x

Solving for variable 'x'.

Reorder the terms:
2 + 9x + -2x + 3x2 = -2 + 2x + 2 + -2x

Combine like terms: 9x + -2x = 7x
2 + 7x + 3x2 = -2 + 2x + 2 + -2x

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

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

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

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


Subproblem 1
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

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 = {-2, -0.3333333333}

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