48n^2-6=-42n

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

Simplifying
48n2 + -6 = -42n

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

Solving
-6 + 48n2 = -42n

Solving for variable 'n'.

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

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

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 7n + 8n2) = 0

Factor a trinomial.
6((-1 + -1n)(1 + -8n)) = 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 '(1 + -8n)' equal to zero and attempt to solve:

Simplifying
1 + -8n = 0

Solving
1 + -8n = 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 + -8n = 0 + -1

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

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

Divide each side by '-8'.
n = 0.125

Simplifying
n = 0.125
Solution
n = {-1, 0.125}