4n^2-11n-78=0

Solution for 4n^2-11n-78=0 equation:

Simplifying
4n2 + -11n + -78 = 0

Reorder the terms:
-78 + -11n + 4n2 = 0

Solving
-78 + -11n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-13 + -4n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -4n)' equal to zero and attempt to solve:

Simplifying
-13 + -4n = 0

Solving
-13 + -4n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -4n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4n = 0 + 13
-4n = 0 + 13

Combine like terms: 0 + 13 = 13
-4n = 13

Divide each side by '-4'.
n = -3.25

Simplifying
n = -3.25
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 = {-3.25, 6}