(18n-12)=3n(3n-1)

Solution for (18n-12)=3n(3n-1) equation:

Simplifying
(18n + -12) = 3n(3n + -1)

Reorder the terms:
(-12 + 18n) = 3n(3n + -1)

Remove parenthesis around (-12 + 18n)
-12 + 18n = 3n(3n + -1)

Reorder the terms:
-12 + 18n = 3n(-1 + 3n)
-12 + 18n = (-1 * 3n + 3n * 3n)
-12 + 18n = (-3n + 9n2)

Solving
-12 + 18n = -3n + 9n2

Solving for variable 'n'.

Combine like terms: 18n + 3n = 21n
-12 + 21n + -9n2 = -3n + 9n2 + 3n + -9n2

Reorder the terms:
-12 + 21n + -9n2 = -3n + 3n + 9n2 + -9n2

Combine like terms: -3n + 3n = 0
-12 + 21n + -9n2 = 0 + 9n2 + -9n2
-12 + 21n + -9n2 = 9n2 + -9n2

Combine like terms: 9n2 + -9n2 = 0
-12 + 21n + -9n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 7n + -3n2) = 0

Factor a trinomial.
3((-4 + 3n)(1 + -1n)) = 0

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

Simplifying
-4 + 3n = 0

Solving
-4 + 3n = 0

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

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

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

Combine like terms: 0 + 4 = 4
3n = 4

Divide each side by '3'.
n = 1.333333333

Simplifying
n = 1.333333333
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 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 + -1n = 0 + -1

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

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

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Solution
n = {1.333333333, 1}