4n^2+15n-54=0

Solution for 4n^2+15n-54=0 equation:

Simplifying
4n2 + 15n + -54 = 0

Reorder the terms:
-54 + 15n + 4n2 = 0

Solving
-54 + 15n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-6 + -1n)(9 + -4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(9 + -4n)' equal to zero and attempt to solve:

Simplifying
9 + -4n = 0

Solving
9 + -4n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4n = 0 + -9
-4n = 0 + -9

Combine like terms: 0 + -9 = -9
-4n = -9

Divide each side by '-4'.
n = 2.25

Simplifying
n = 2.25
Solution
n = {-6, 2.25}