(3x+2)(3x+2)-9=0

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Solution for (3x+2)(3x+2)-9=0 equation: 


Simplifying
(3x + 2)(3x + 2) + -9 = 0

Reorder the terms:
(2 + 3x)(3x + 2) + -9 = 0

Reorder the terms:
(2 + 3x)(2 + 3x) + -9 = 0

Multiply (2 + 3x) * (2 + 3x)
(2(2 + 3x) + 3x * (2 + 3x)) + -9 = 0
((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + -9 = 0
((4 + 6x) + 3x * (2 + 3x)) + -9 = 0
(4 + 6x + (2 * 3x + 3x * 3x)) + -9 = 0
(4 + 6x + (6x + 9x2)) + -9 = 0

Combine like terms: 6x + 6x = 12x
(4 + 12x + 9x2) + -9 = 0

Reorder the terms:
4 + -9 + 12x + 9x2 = 0

Combine like terms: 4 + -9 = -5
-5 + 12x + 9x2 = 0

Solving
-5 + 12x + 9x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + -3x)(1 + -3x) = 0


Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3x = 0 + 5
-3x = 0 + 5

Combine like terms: 0 + 5 = 5
-3x = 5

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667

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 = {-1.666666667, 0.3333333333}

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