15n^2+16n-21=-6

Solution for 15n^2+16n-21=-6 equation:

Simplifying
15n2 + 16n + -21 = -6

Reorder the terms:
-21 + 16n + 15n2 = -6

Solving
-21 + 16n + 15n2 = -6

Solving for variable 'n'.

Reorder the terms:
-21 + 6 + 16n + 15n2 = -6 + 6

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

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

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

Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve:

Simplifying
-5 + -3n = 0

Solving
-5 + -3n = 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 + -3n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3n = 0 + 5
-3n = 0 + 5

Combine like terms: 0 + 5 = 5
-3n = 5

Divide each side by '-3'.
n = -1.666666667

Simplifying
n = -1.666666667
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 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 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {-1.666666667, 0.6}