30n^2-192n+180=-6n

Solution for 30n^2-192n+180=-6n equation:

Simplifying
30n2 + -192n + 180 = -6n

Reorder the terms:
180 + -192n + 30n2 = -6n

Solving
180 + -192n + 30n2 = -6n

Solving for variable 'n'.

Reorder the terms:
180 + -192n + 6n + 30n2 = -6n + 6n

Combine like terms: -192n + 6n = -186n
180 + -186n + 30n2 = -6n + 6n

Combine like terms: -6n + 6n = 0
180 + -186n + 30n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(30 + -31n + 5n2) = 0

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

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

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

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

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

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

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

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

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {1.2, 5}