(3n-1)(3n-1)=12n+8

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Solution for (3n-1)(3n-1)=12n+8 equation: 


Simplifying
(3n + -1)(3n + -1) = 12n + 8

Reorder the terms:
(-1 + 3n)(3n + -1) = 12n + 8

Reorder the terms:
(-1 + 3n)(-1 + 3n) = 12n + 8

Multiply (-1 + 3n) * (-1 + 3n)
(-1(-1 + 3n) + 3n * (-1 + 3n)) = 12n + 8
((-1 * -1 + 3n * -1) + 3n * (-1 + 3n)) = 12n + 8
((1 + -3n) + 3n * (-1 + 3n)) = 12n + 8
(1 + -3n + (-1 * 3n + 3n * 3n)) = 12n + 8
(1 + -3n + (-3n + 9n2)) = 12n + 8

Combine like terms: -3n + -3n = -6n
(1 + -6n + 9n2) = 12n + 8

Reorder the terms:
1 + -6n + 9n2 = 8 + 12n

Solving
1 + -6n + 9n2 = 8 + 12n

Solving for variable 'n'.

Reorder the terms:
1 + -8 + -6n + -12n + 9n2 = 8 + 12n + -8 + -12n

Combine like terms: 1 + -8 = -7
-7 + -6n + -12n + 9n2 = 8 + 12n + -8 + -12n

Combine like terms: -6n + -12n = -18n
-7 + -18n + 9n2 = 8 + 12n + -8 + -12n

Reorder the terms:
-7 + -18n + 9n2 = 8 + -8 + 12n + -12n

Combine like terms: 8 + -8 = 0
-7 + -18n + 9n2 = 0 + 12n + -12n
-7 + -18n + 9n2 = 12n + -12n

Combine like terms: 12n + -12n = 0
-7 + -18n + 9n2 = 0

Factor a trinomial.
(-1 + -3n)(7 + -3n) = 0


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

Simplifying
-1 + -3n = 0

Solving
-1 + -3n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3n = 0 + 1
-3n = 0 + 1

Combine like terms: 0 + 1 = 1
-3n = 1

Divide each side by '-3'.
n = -0.3333333333

Simplifying
n = -0.3333333333

Subproblem 2
Set the factor '(7 + -3n)' equal to zero and attempt to solve:

Simplifying
7 + -3n = 0

Solving
7 + -3n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3n = 0 + -7
-3n = 0 + -7

Combine like terms: 0 + -7 = -7
-3n = -7

Divide each side by '-3'.
n = 2.333333333

Simplifying
n = 2.333333333
Solution
n = {-0.3333333333, 2.333333333}

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