7n^2-63n+138=-2

Solution for 7n^2-63n+138=-2 equation:

Simplifying
7n2 + -63n + 138 = -2

Reorder the terms:
138 + -63n + 7n2 = -2

Solving
138 + -63n + 7n2 = -2

Solving for variable 'n'.

Reorder the terms:
138 + 2 + -63n + 7n2 = -2 + 2

Combine like terms: 138 + 2 = 140
140 + -63n + 7n2 = -2 + 2

Combine like terms: -2 + 2 = 0
140 + -63n + 7n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(20 + -9n + n2) = 0

Factor a trinomial.
7((4 + -1n)(5 + -1n)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {4, 5}