8n^2+42n+27=0

Solution for 8n^2+42n+27=0 equation:

Simplifying
8n2 + 42n + 27 = 0

Reorder the terms:
27 + 42n + 8n2 = 0

Solving
27 + 42n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(9 + 2n)(3 + 4n) = 0

Subproblem 1
Set the factor '(9 + 2n)' equal to zero and attempt to solve:

Simplifying
9 + 2n = 0

Solving
9 + 2n = 0

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

Add '-9' to each side of the equation.
9 + -9 + 2n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2n = 0 + -9
2n = 0 + -9

Combine like terms: 0 + -9 = -9
2n = -9

Divide each side by '2'.
n = -4.5

Simplifying
n = -4.5
Subproblem 2
Set the factor '(3 + 4n)' equal to zero and attempt to solve:

Simplifying
3 + 4n = 0

Solving
3 + 4n = 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 + 4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4n = 0 + -3
4n = 0 + -3

Combine like terms: 0 + -3 = -3
4n = -3

Divide each side by '4'.
n = -0.75

Simplifying
n = -0.75
Solution
n = {-4.5, -0.75}