18n^2-15=3n

Solution for 18n^2-15=3n equation:

Simplifying
18n2 + -15 = 3n

Reorder the terms:
-15 + 18n2 = 3n

Solving
-15 + 18n2 = 3n

Solving for variable 'n'.

Reorder the terms:
-15 + -3n + 18n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-15 + -3n + 18n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1n + 6n2) = 0

Factor a trinomial.
3((-5 + -6n)(1 + -1n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -6n)' equal to zero and attempt to solve:

Simplifying
-5 + -6n = 0

Solving
-5 + -6n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -6n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6n = 0 + 5
-6n = 0 + 5

Combine like terms: 0 + 5 = 5
-6n = 5

Divide each side by '-6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
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 = {-0.8333333333, 1}