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

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


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

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

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

Multiply (2 + 3x) * (6 + 3x)
(2(6 + 3x) + 3x * (6 + 3x)) = 0
((6 * 2 + 3x * 2) + 3x * (6 + 3x)) = 0
((12 + 6x) + 3x * (6 + 3x)) = 0
(12 + 6x + (6 * 3x + 3x * 3x)) = 0
(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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