3x(3x+2)+6(3x+2)=0

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Solution for 3x(3x+2)+6(3x+2)=0 equation: 


Simplifying
3x(3x + 2) + 6(3x + 2) = 0

Reorder the terms:
3x(2 + 3x) + 6(3x + 2) = 0
(2 * 3x + 3x * 3x) + 6(3x + 2) = 0
(6x + 9x2) + 6(3x + 2) = 0

Reorder the terms:
6x + 9x2 + 6(2 + 3x) = 0
6x + 9x2 + (2 * 6 + 3x * 6) = 0
6x + 9x2 + (12 + 18x) = 0

Reorder the terms:
12 + 6x + 18x + 9x2 = 0

Combine like terms: 6x + 18x = 24x
12 + 24x + 9x2 = 0

Solving
12 + 24x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 8x + 3x2) = 0

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

Ignore the factor 3.

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 '(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 = {-2, -0.6666666667}

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