5n^2+12=19n

Solution for 5n^2+12=19n equation:

Simplifying
5n2 + 12 = 19n

Reorder the terms:
12 + 5n2 = 19n

Solving
12 + 5n2 = 19n

Solving for variable 'n'.

Reorder the terms:
12 + -19n + 5n2 = 19n + -19n

Combine like terms: 19n + -19n = 0
12 + -19n + 5n2 = 0

Factor a trinomial.
(4 + -5n)(3 + -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 '(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 = {0.8, 3}