(5n-3)(4-3n)=0

Solution for (5n-3)(4-3n)=0 equation:

Simplifying
(5n + -3)(4 + -3n) = 0

Reorder the terms:
(-3 + 5n)(4 + -3n) = 0

Multiply (-3 + 5n) * (4 + -3n)
(-3(4 + -3n) + 5n * (4 + -3n)) = 0
((4 * -3 + -3n * -3) + 5n * (4 + -3n)) = 0
((-12 + 9n) + 5n * (4 + -3n)) = 0
(-12 + 9n + (4 * 5n + -3n * 5n)) = 0
(-12 + 9n + (20n + -15n2)) = 0

Combine like terms: 9n + 20n = 29n
(-12 + 29n + -15n2) = 0

Solving
-12 + 29n + -15n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + 3n)(3 + -5n) = 0

Subproblem 1
Set the factor '(-4 + 3n)' equal to zero and attempt to solve:

Simplifying
-4 + 3n = 0

Solving
-4 + 3n = 0

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

Add '4' to each side of the equation.
-4 + 4 + 3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3n = 0 + 4
3n = 0 + 4

Combine like terms: 0 + 4 = 4
3n = 4

Divide each side by '3'.
n = 1.333333333

Simplifying
n = 1.333333333
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {1.333333333, 0.6}