45n^2-51n-120=6

Solution for 45n^2-51n-120=6 equation:

Simplifying
45n2 + -51n + -120 = 6

Reorder the terms:
-120 + -51n + 45n2 = 6

Solving
-120 + -51n + 45n2 = 6

Solving for variable 'n'.

Reorder the terms:
-120 + -6 + -51n + 45n2 = 6 + -6

Combine like terms: -120 + -6 = -126
-126 + -51n + 45n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-126 + -51n + 45n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-42 + -17n + 15n2) = 0

Factor a trinomial.
3((-6 + -5n)(7 + -3n)) = 0

Ignore the factor 3.
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 '(7 + -3n)' equal to zero and attempt to solve:

Simplifying
7 + -3n = 0

Solving
7 + -3n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -3n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3n = 0 + -7
-3n = 0 + -7

Combine like terms: 0 + -7 = -7
-3n = -7

Divide each side by '-3'.
n = 2.333333333

Simplifying
n = 2.333333333
Solution
n = {-1.2, 2.333333333}