30n^2+84n-18=0

Solution for 30n^2+84n-18=0 equation:

Simplifying
30n2 + 84n + -18 = 0

Reorder the terms:
-18 + 84n + 30n2 = 0

Solving
-18 + 84n + 30n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 14n + 5n2) = 0

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

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

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

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

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve:

Simplifying
1 + -5n = 0

Solving
1 + -5n = 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 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-3, 0.2}