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

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

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

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

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

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

Combine like terms: -15n + 4n = -11n
(-12 + -11n + 5n2) = 0

Solving
-12 + -11n + 5n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-4 + -5n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve:

Simplifying
-4 + -5n = 0

Solving
-4 + -5n = 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 + -5n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5n = 0 + 4
-5n = 0 + 4

Combine like terms: 0 + 4 = 4
-5n = 4

Divide each side by '-5'.
n = -0.8

Simplifying
n = -0.8
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.8, 3}