3(n^2)-13n=30

Solution for 3(n^2)-13n=30 equation:

Simplifying
3(n2) + -13n = 30

Reorder the terms:
-13n + 3n2 = 30

Solving
-13n + 3n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -13n + 3n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -13n + 3n2 = 0

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

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

Simplifying
-5 + -3n = 0

Solving
-5 + -3n = 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 + -3n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3n = 0 + 5
-3n = 0 + 5

Combine like terms: 0 + 5 = 5
-3n = 5

Divide each side by '-3'.
n = -1.666666667

Simplifying
n = -1.666666667
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 = {-1.666666667, 6}