n(4n^2-19n-30)=0

Solution for n(4n^2-19n-30)=0 equation:

Simplifying
n(4n2 + -19n + -30) = 0

Reorder the terms:
n(-30 + -19n + 4n2) = 0
(-30 * n + -19n * n + 4n2 * n) = 0
(-30n + -19n2 + 4n3) = 0

Solving
-30n + -19n2 + 4n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n'.
n(-30 + -19n + 4n2) = 0

Factor a trinomial.
n((-5 + -4n)(6 + -1n)) = 0

Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

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

Simplifying
n = 0
Subproblem 2
Set the factor '(-5 + -4n)' equal to zero and attempt to solve:

Simplifying
-5 + -4n = 0

Solving
-5 + -4n = 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 + -4n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4n = 0 + 5
-4n = 0 + 5

Combine like terms: 0 + 5 = 5
-4n = 5

Divide each side by '-4'.
n = -1.25

Simplifying
n = -1.25
Subproblem 3
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 = {0, -1.25, 6}