n(5n+11)=36

Solution for n(5n+11)=36 equation:

Simplifying
n(5n + 11) = 36

Reorder the terms:
n(11 + 5n) = 36
(11 * n + 5n * n) = 36
(11n + 5n2) = 36

Solving
11n + 5n2 = 36

Solving for variable 'n'.

Reorder the terms:
-36 + 11n + 5n2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 11n + 5n2 = 0

Factor a trinomial.
(-4 + -1n)(9 + -5n) = 0

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

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(9 + -5n)' equal to zero and attempt to solve:

Simplifying
9 + -5n = 0

Solving
9 + -5n = 0

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

Add '-9' to each side of the equation.
9 + -9 + -5n = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -5n = 0 + -9
-5n = 0 + -9

Combine like terms: 0 + -9 = -9
-5n = -9

Divide each side by '-5'.
n = 1.8

Simplifying
n = 1.8
Solution
n = {-4, 1.8}