8n^2+40=-69n

Solution for 8n^2+40=-69n equation:

Simplifying
8n2 + 40 = -69n

Reorder the terms:
40 + 8n2 = -69n

Solving
40 + 8n2 = -69n

Solving for variable 'n'.

Reorder the terms:
40 + 69n + 8n2 = -69n + 69n

Combine like terms: -69n + 69n = 0
40 + 69n + 8n2 = 0

Factor a trinomial.
(8 + n)(5 + 8n) = 0

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

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

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

Simplifying
n = -8
Subproblem 2
Set the factor '(5 + 8n)' equal to zero and attempt to solve:

Simplifying
5 + 8n = 0

Solving
5 + 8n = 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 + 8n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8n = 0 + -5
8n = 0 + -5

Combine like terms: 0 + -5 = -5
8n = -5

Divide each side by '8'.
n = -0.625

Simplifying
n = -0.625
Solution
n = {-8, -0.625}