-n^2+7n+93=6n+3

Solution for -n^2+7n+93=6n+3 equation:

Simplifying
-1n2 + 7n + 93 = 6n + 3

Reorder the terms:
93 + 7n + -1n2 = 6n + 3

Reorder the terms:
93 + 7n + -1n2 = 3 + 6n

Solving
93 + 7n + -1n2 = 3 + 6n

Solving for variable 'n'.

Reorder the terms:
93 + -3 + 7n + -6n + -1n2 = 3 + 6n + -3 + -6n

Combine like terms: 93 + -3 = 90
90 + 7n + -6n + -1n2 = 3 + 6n + -3 + -6n

Combine like terms: 7n + -6n = 1n
90 + 1n + -1n2 = 3 + 6n + -3 + -6n

Reorder the terms:
90 + 1n + -1n2 = 3 + -3 + 6n + -6n

Combine like terms: 3 + -3 = 0
90 + 1n + -1n2 = 0 + 6n + -6n
90 + 1n + -1n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
90 + 1n + -1n2 = 0

Factor a trinomial.
(10 + -1n)(9 + n) = 0

Subproblem 1
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Subproblem 2
Set the factor '(9 + n)' equal to zero and attempt to solve:

Simplifying
9 + n = 0

Solving
9 + n = 0

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

Add '-9' to each side of the equation.
9 + -9 + n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + n = 0 + -9
n = 0 + -9

Combine like terms: 0 + -9 = -9
n = -9

Simplifying
n = -9
Solution
n = {10, -9}