5n^2+14=37n

Solution for 5n^2+14=37n equation:

Simplifying
5n2 + 14 = 37n

Reorder the terms:
14 + 5n2 = 37n

Solving
14 + 5n2 = 37n

Solving for variable 'n'.

Reorder the terms:
14 + -37n + 5n2 = 37n + -37n

Combine like terms: 37n + -37n = 0
14 + -37n + 5n2 = 0

Factor a trinomial.
(2 + -5n)(7 + -1n) = 0

Subproblem 1
Set the factor '(2 + -5n)' equal to zero and attempt to solve:

Simplifying
2 + -5n = 0

Solving
2 + -5n = 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 + -5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5n = 0 + -2
-5n = 0 + -2

Combine like terms: 0 + -2 = -2
-5n = -2

Divide each side by '-5'.
n = 0.4

Simplifying
n = 0.4
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {0.4, 7}