6n^2=48n-42

Solution for 6n^2=48n-42 equation:

Simplifying
6n2 = 48n + -42

Reorder the terms:
6n2 = -42 + 48n

Solving
6n2 = -42 + 48n

Solving for variable 'n'.

Reorder the terms:
42 + -48n + 6n2 = -42 + 48n + 42 + -48n

Reorder the terms:
42 + -48n + 6n2 = -42 + 42 + 48n + -48n

Combine like terms: -42 + 42 = 0
42 + -48n + 6n2 = 0 + 48n + -48n
42 + -48n + 6n2 = 48n + -48n

Combine like terms: 48n + -48n = 0
42 + -48n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + -8n + n2) = 0

Factor a trinomial.
6((1 + -1n)(7 + -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 '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {1, 7}