5n^2+8=14n

Solution for 5n^2+8=14n equation:

Simplifying
5n2 + 8 = 14n

Reorder the terms:
8 + 5n2 = 14n

Solving
8 + 5n2 = 14n

Solving for variable 'n'.

Reorder the terms:
8 + -14n + 5n2 = 14n + -14n

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

Factor a trinomial.
(4 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(4 + -5n)' equal to zero and attempt to solve:

Simplifying
4 + -5n = 0

Solving
4 + -5n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5n = 0 + -4
-5n = 0 + -4

Combine like terms: 0 + -4 = -4
-5n = -4

Divide each side by '-5'.
n = 0.8

Simplifying
n = 0.8
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

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

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

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.8, 2}