14n^2-23n+13=5

Solution for 14n^2-23n+13=5 equation:

Simplifying
14n2 + -23n + 13 = 5

Reorder the terms:
13 + -23n + 14n2 = 5

Solving
13 + -23n + 14n2 = 5

Solving for variable 'n'.

Reorder the terms:
13 + -5 + -23n + 14n2 = 5 + -5

Combine like terms: 13 + -5 = 8
8 + -23n + 14n2 = 5 + -5

Combine like terms: 5 + -5 = 0
8 + -23n + 14n2 = 0

Factor a trinomial.
(1 + -2n)(8 + -7n) = 0

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Subproblem 2
Set the factor '(8 + -7n)' equal to zero and attempt to solve:

Simplifying
8 + -7n = 0

Solving
8 + -7n = 0

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

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

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

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

Divide each side by '-7'.
n = 1.142857143

Simplifying
n = 1.142857143
Solution
n = {0.5, 1.142857143}