4n(n+8)=36

Solution for 4n(n+8)=36 equation:

Simplifying
4n(n + 8) = 36

Reorder the terms:
4n(8 + n) = 36
(8 * 4n + n * 4n) = 36
(32n + 4n2) = 36

Solving
32n + 4n2 = 36

Solving for variable 'n'.

Reorder the terms:
-36 + 32n + 4n2 = 36 + -36

Combine like terms: 36 + -36 = 0
-36 + 32n + 4n2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 8n + n2) = 0

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

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + -1n)' equal to zero and attempt to solve:

Simplifying
-9 + -1n = 0

Solving
-9 + -1n = 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 + -1n = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1n = 0 + 9
-1n = 0 + 9

Combine like terms: 0 + 9 = 9
-1n = 9

Divide each side by '-1'.
n = -9

Simplifying
n = -9
Subproblem 2
Set the factor '(1 + -1n)' equal to zero and attempt to solve:

Simplifying
1 + -1n = 0

Solving
1 + -1n = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1n = 0 + -1

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

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

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

Simplifying
n = 1
Solution
n = {-9, 1}