(5n+6)(4n+8)=

Solution for (5n+6)(4n+8)= equation:

Simplifying
(5n + 6)(4n + 8) = 0

Reorder the terms:
(6 + 5n)(4n + 8) = 0

Reorder the terms:
(6 + 5n)(8 + 4n) = 0

Multiply (6 + 5n) * (8 + 4n)
(6(8 + 4n) + 5n * (8 + 4n)) = 0
((8 * 6 + 4n * 6) + 5n * (8 + 4n)) = 0
((48 + 24n) + 5n * (8 + 4n)) = 0
(48 + 24n + (8 * 5n + 4n * 5n)) = 0
(48 + 24n + (40n + 20n2)) = 0

Combine like terms: 24n + 40n = 64n
(48 + 64n + 20n2) = 0

Solving
48 + 64n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(12 + 16n + 5n2) = 0

Factor a trinomial.
4((2 + n)(6 + 5n)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 0

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

Add '-2' to each side of the equation.
2 + -2 + n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + n = 0 + -2
n = 0 + -2

Combine like terms: 0 + -2 = -2
n = -2

Simplifying
n = -2
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 = {-2, -1.2}