(n-11)(4n+5)=0

Solution for (n-11)(4n+5)=0 equation:

Simplifying
(n + -11)(4n + 5) = 0

Reorder the terms:
(-11 + n)(4n + 5) = 0

Reorder the terms:
(-11 + n)(5 + 4n) = 0

Multiply (-11 + n) * (5 + 4n)
(-11(5 + 4n) + n(5 + 4n)) = 0
((5 * -11 + 4n * -11) + n(5 + 4n)) = 0
((-55 + -44n) + n(5 + 4n)) = 0
(-55 + -44n + (5 * n + 4n * n)) = 0
(-55 + -44n + (5n + 4n2)) = 0

Combine like terms: -44n + 5n = -39n
(-55 + -39n + 4n2) = 0

Solving
-55 + -39n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -4n)(11 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -4n)' equal to zero and attempt to solve:

Simplifying
-5 + -4n = 0

Solving
-5 + -4n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4n = 0 + 5
-4n = 0 + 5

Combine like terms: 0 + 5 = 5
-4n = 5

Divide each side by '-4'.
n = -1.25

Simplifying
n = -1.25
Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-1.25, 11}