8n^2+51n+15=-3

Solution for 8n^2+51n+15=-3 equation:

Simplifying
8n2 + 51n + 15 = -3

Reorder the terms:
15 + 51n + 8n2 = -3

Solving
15 + 51n + 8n2 = -3

Solving for variable 'n'.

Reorder the terms:
15 + 3 + 51n + 8n2 = -3 + 3

Combine like terms: 15 + 3 = 18
18 + 51n + 8n2 = -3 + 3

Combine like terms: -3 + 3 = 0
18 + 51n + 8n2 = 0

Factor a trinomial.
(6 + n)(3 + 8n) = 0

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(3 + 8n)' equal to zero and attempt to solve:

Simplifying
3 + 8n = 0

Solving
3 + 8n = 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 + 8n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 8n = 0 + -3
8n = 0 + -3

Combine like terms: 0 + -3 = -3
8n = -3

Divide each side by '8'.
n = -0.375

Simplifying
n = -0.375
Solution
n = {-6, -0.375}