8n^2-78n+19=0

Solution for 8n^2-78n+19=0 equation:

Simplifying
8n2 + -78n + 19 = 0

Reorder the terms:
19 + -78n + 8n2 = 0

Solving
19 + -78n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -4n)(19 + -2n) = 0

Subproblem 1
Set the factor '(1 + -4n)' equal to zero and attempt to solve:

Simplifying
1 + -4n = 0

Solving
1 + -4n = 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 + -4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4n = 0 + -1
-4n = 0 + -1

Combine like terms: 0 + -1 = -1
-4n = -1

Divide each side by '-4'.
n = 0.25

Simplifying
n = 0.25
Subproblem 2
Set the factor '(19 + -2n)' equal to zero and attempt to solve:

Simplifying
19 + -2n = 0

Solving
19 + -2n = 0

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

Add '-19' to each side of the equation.
19 + -19 + -2n = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -2n = 0 + -19
-2n = 0 + -19

Combine like terms: 0 + -19 = -19
-2n = -19

Divide each side by '-2'.
n = 9.5

Simplifying
n = 9.5
Solution
n = {0.25, 9.5}