8n(n+3)=2n-15

Solution for 8n(n+3)=2n-15 equation:

Simplifying
8n(n + 3) = 2n + -15

Reorder the terms:
8n(3 + n) = 2n + -15
(3 * 8n + n * 8n) = 2n + -15
(24n + 8n2) = 2n + -15

Reorder the terms:
24n + 8n2 = -15 + 2n

Solving
24n + 8n2 = -15 + 2n

Solving for variable 'n'.

Reorder the terms:
15 + 24n + -2n + 8n2 = -15 + 2n + 15 + -2n

Combine like terms: 24n + -2n = 22n
15 + 22n + 8n2 = -15 + 2n + 15 + -2n

Reorder the terms:
15 + 22n + 8n2 = -15 + 15 + 2n + -2n

Combine like terms: -15 + 15 = 0
15 + 22n + 8n2 = 0 + 2n + -2n
15 + 22n + 8n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
15 + 22n + 8n2 = 0

Factor a trinomial.
(3 + 2n)(5 + 4n) = 0

Subproblem 1
Set the factor '(3 + 2n)' equal to zero and attempt to solve:

Simplifying
3 + 2n = 0

Solving
3 + 2n = 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 + 2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2n = 0 + -3
2n = 0 + -3

Combine like terms: 0 + -3 = -3
2n = -3

Divide each side by '2'.
n = -1.5

Simplifying
n = -1.5
Subproblem 2
Set the factor '(5 + 4n)' equal to zero and attempt to solve:

Simplifying
5 + 4n = 0

Solving
5 + 4n = 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 + 4n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4n = 0 + -5
4n = 0 + -5

Combine like terms: 0 + -5 = -5
4n = -5

Divide each side by '4'.
n = -1.25

Simplifying
n = -1.25
Solution
n = {-1.5, -1.25}