3n^2-8n=60

Solution for 3n^2-8n=60 equation:

Simplifying
3n2 + -8n = 60

Reorder the terms:
-8n + 3n2 = 60

Solving
-8n + 3n2 = 60

Solving for variable 'n'.

Reorder the terms:
-60 + -8n + 3n2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + -8n + 3n2 = 0

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

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

Simplifying
-10 + -3n = 0

Solving
-10 + -3n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3n = 0 + 10
-3n = 0 + 10

Combine like terms: 0 + 10 = 10
-3n = 10

Divide each side by '-3'.
n = -3.333333333

Simplifying
n = -3.333333333
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 = {-3.333333333, 6}