4n^2-8n-45=0

Solution for 4n^2-8n-45=0 equation:

Simplifying
4n2 + -8n + -45 = 0

Reorder the terms:
-45 + -8n + 4n2 = 0

Solving
-45 + -8n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -2n)(9 + -2n) = 0

Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 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 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
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
Solution
n = {-2.5, 4.5}