5n^2+13n=6

Solution for 5n^2+13n=6 equation:

Simplifying
5n2 + 13n = 6

Reorder the terms:
13n + 5n2 = 6

Solving
13n + 5n2 = 6

Solving for variable 'n'.

Reorder the terms:
-6 + 13n + 5n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 13n + 5n2 = 0

Factor a trinomial.
(-3 + -1n)(2 + -5n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-3, 0.4}