8n^2+46n+45=0

Solution for 8n^2+46n+45=0 equation:

Simplifying
8n2 + 46n + 45 = 0

Reorder the terms:
45 + 46n + 8n2 = 0

Solving
45 + 46n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(9 + 2n)(5 + 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 '(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 = {-4.5, -1.25}