6n^2-54n=-48

Solution for 6n^2-54n=-48 equation:

Simplifying
6n2 + -54n = -48

Reorder the terms:
-54n + 6n2 = -48

Solving
-54n + 6n2 = -48

Solving for variable 'n'.

Reorder the terms:
48 + -54n + 6n2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + -54n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(8 + -9n + n2) = 0

Factor a trinomial.
6((1 + -1n)(8 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1n = 0 + -1
-1n = 0 + -1

Combine like terms: 0 + -1 = -1
-1n = -1

Divide each side by '-1'.
n = 1

Simplifying
n = 1
Subproblem 2
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8
Solution
n = {1, 8}