(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 = -16n
(-48 + -16n + 20n2) = 0

Solving
-48 + -16n + 20n2 = 0

Solving for variable 'n'.

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

Factor a trinomial.
4((-6 + -5n)(2 + -1n)) = 0

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

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