5n^2-19n=30

Solution for 5n^2-19n=30 equation:

Simplifying
5n2 + -19n = 30

Reorder the terms:
-19n + 5n2 = 30

Solving
-19n + 5n2 = 30

Solving for variable 'n'.

Reorder the terms:
-30 + -19n + 5n2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -19n + 5n2 = 0

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

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}