8n^2-31n+21=0

Solution for 8n^2-31n+21=0 equation:

Simplifying
8n2 + -31n + 21 = 0

Reorder the terms:
21 + -31n + 8n2 = 0

Solving
21 + -31n + 8n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(7 + -8n)(3 + -1n) = 0

Subproblem 1
Set the factor '(7 + -8n)' equal to zero and attempt to solve:

Simplifying
7 + -8n = 0

Solving
7 + -8n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8n = 0 + -7
-8n = 0 + -7

Combine like terms: 0 + -7 = -7
-8n = -7

Divide each side by '-8'.
n = 0.875

Simplifying
n = 0.875
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.875, 3}