(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.
(-2 + -3x)(4 + -3x) = 0


Subproblem 1
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

Subproblem 2
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
Solution
x = {-0.6666666667, 1.333333333}

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