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

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

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

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

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

Multiply (6 + 5n) * (5 + 4n)
(6(5 + 4n) + 5n * (5 + 4n)) = 0
((5 * 6 + 4n * 6) + 5n * (5 + 4n)) = 0
((30 + 24n) + 5n * (5 + 4n)) = 0
(30 + 24n + (5 * 5n + 4n * 5n)) = 0
(30 + 24n + (25n + 20n2)) = 0

Combine like terms: 24n + 25n = 49n
(30 + 49n + 20n2) = 0

Solving
30 + 49n + 20n2 = 0

Solving for variable 'n'.

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

Simplifying
6 + 5n = 0

Solving
6 + 5n = 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 + 5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 5n = 0 + -6
5n = 0 + -6

Combine like terms: 0 + -6 = -6
5n = -6

Divide each side by '5'.
n = -1.2

Simplifying
n = -1.2
Solution
n = {-1.25, -1.2}