(3x+1)(3x+1)=9

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Solution for (3x+1)(3x+1)=9 equation: 


Simplifying
(3x + 1)(3x + 1) = 9

Reorder the terms:
(1 + 3x)(3x + 1) = 9

Reorder the terms:
(1 + 3x)(1 + 3x) = 9

Multiply (1 + 3x) * (1 + 3x)
(1(1 + 3x) + 3x * (1 + 3x)) = 9
((1 * 1 + 3x * 1) + 3x * (1 + 3x)) = 9
((1 + 3x) + 3x * (1 + 3x)) = 9
(1 + 3x + (1 * 3x + 3x * 3x)) = 9
(1 + 3x + (3x + 9x2)) = 9

Combine like terms: 3x + 3x = 6x
(1 + 6x + 9x2) = 9

Solving
1 + 6x + 9x2 = 9

Solving for variable 'x'.

Reorder the terms:
1 + -9 + 6x + 9x2 = 9 + -9

Combine like terms: 1 + -9 = -8
-8 + 6x + 9x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-8 + 6x + 9x2 = 0

Factor a trinomial.
(-4 + -3x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 0.6666666667}

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