30n^2-20n=960

Solution for 30n^2-20n=960 equation:

Simplifying
30n2 + -20n = 960

Reorder the terms:
-20n + 30n2 = 960

Solving
-20n + 30n2 = 960

Solving for variable 'n'.

Reorder the terms:
-960 + -20n + 30n2 = 960 + -960

Combine like terms: 960 + -960 = 0
-960 + -20n + 30n2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-96 + -2n + 3n2) = 0

Factor a trinomial.
10((-16 + -3n)(6 + -1n)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-16 + -3n)' equal to zero and attempt to solve:

Simplifying
-16 + -3n = 0

Solving
-16 + -3n = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3n = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3n = 0 + 16
-3n = 0 + 16

Combine like terms: 0 + 16 = 16
-3n = 16

Divide each side by '-3'.
n = -5.333333333

Simplifying
n = -5.333333333
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-5.333333333, 6}