4n^2-9n-5=-8n

Solution for 4n^2-9n-5=-8n equation:

Simplifying
4n2 + -9n + -5 = -8n

Reorder the terms:
-5 + -9n + 4n2 = -8n

Solving
-5 + -9n + 4n2 = -8n

Solving for variable 'n'.

Reorder the terms:
-5 + -9n + 8n + 4n2 = -8n + 8n

Combine like terms: -9n + 8n = -1n
-5 + -1n + 4n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
-5 + -1n + 4n2 = 0

Factor a trinomial.
(-1 + -1n)(5 + -4n) = 0

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1n = 0 + 1
-1n = 0 + 1

Combine like terms: 0 + 1 = 1
-1n = 1

Divide each side by '-1'.
n = -1

Simplifying
n = -1
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, 1.25}