6n^2+3n=18

Solution for 6n^2+3n=18 equation:

Simplifying
6n2 + 3n = 18

Reorder the terms:
3n + 6n2 = 18

Solving
3n + 6n2 = 18

Solving for variable 'n'.

Reorder the terms:
-18 + 3n + 6n2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + 3n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + n + 2n2) = 0

Factor a trinomial.
3((-2 + -1n)(3 + -2n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-2 + -1n)' equal to zero and attempt to solve:

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1n = 0 + 2
-1n = 0 + 2

Combine like terms: 0 + 2 = 2
-1n = 2

Divide each side by '-1'.
n = -2

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-2, 1.5}