(4n+5)(n-6)=0

Solution for (4n+5)(n-6)=0 equation:

Simplifying
(4n + 5)(n + -6) = 0

Reorder the terms:
(5 + 4n)(n + -6) = 0

Reorder the terms:
(5 + 4n)(-6 + n) = 0

Multiply (5 + 4n) * (-6 + n)
(5(-6 + n) + 4n * (-6 + n)) = 0
((-6 * 5 + n * 5) + 4n * (-6 + n)) = 0
((-30 + 5n) + 4n * (-6 + n)) = 0
(-30 + 5n + (-6 * 4n + n * 4n)) = 0
(-30 + 5n + (-24n + 4n2)) = 0

Combine like terms: 5n + -24n = -19n
(-30 + -19n + 4n2) = 0

Solving
-30 + -19n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -4n)(6 + -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 '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-1.25, 6}