7n^2+16n-21=-6

Solution for 7n^2+16n-21=-6 equation:

Simplifying
7n2 + 16n + -21 = -6

Reorder the terms:
-21 + 16n + 7n2 = -6

Solving
-21 + 16n + 7n2 = -6

Solving for variable 'n'.

Reorder the terms:
-21 + 6 + 16n + 7n2 = -6 + 6

Combine like terms: -21 + 6 = -15
-15 + 16n + 7n2 = -6 + 6

Combine like terms: -6 + 6 = 0
-15 + 16n + 7n2 = 0

Factor a trinomial.
(-3 + -1n)(5 + -7n) = 0

Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve:

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(5 + -7n)' equal to zero and attempt to solve:

Simplifying
5 + -7n = 0

Solving
5 + -7n = 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 + -7n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7n = 0 + -5
-7n = 0 + -5

Combine like terms: 0 + -5 = -5
-7n = -5

Divide each side by '-7'.
n = 0.7142857143

Simplifying
n = 0.7142857143
Solution
n = {-3, 0.7142857143}