5n^2+3n=26

Solution for 5n^2+3n=26 equation:

Simplifying
5n2 + 3n = 26

Reorder the terms:
3n + 5n2 = 26

Solving
3n + 5n2 = 26

Solving for variable 'n'.

Reorder the terms:
-26 + 3n + 5n2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 3n + 5n2 = 0

Factor a trinomial.
(-13 + -5n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -5n)' equal to zero and attempt to solve:

Simplifying
-13 + -5n = 0

Solving
-13 + -5n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -5n = 0 + 13

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

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

Divide each side by '-5'.
n = -2.6

Simplifying
n = -2.6
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 = {-2.6, 2}