(4N+3)(5N+1)=0

Solution for (4N+3)(5N+1)=0 equation:

Simplifying
(4N + 3)(5N + 1) = 0

Reorder the terms:
(3 + 4N)(5N + 1) = 0

Reorder the terms:
(3 + 4N)(1 + 5N) = 0

Multiply (3 + 4N) * (1 + 5N)
(3(1 + 5N) + 4N * (1 + 5N)) = 0
((1 * 3 + 5N * 3) + 4N * (1 + 5N)) = 0
((3 + 15N) + 4N * (1 + 5N)) = 0
(3 + 15N + (1 * 4N + 5N * 4N)) = 0
(3 + 15N + (4N + 20N2)) = 0

Combine like terms: 15N + 4N = 19N
(3 + 19N + 20N2) = 0

Solving
3 + 19N + 20N2 = 0

Solving for variable 'N'.

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

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

Simplifying
3 + 4N = 0

Solving
3 + 4N = 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 + 4N = 0 + -3

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

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

Divide each side by '4'.
N = -0.75

Simplifying
N = -0.75
Subproblem 2
Set the factor '(1 + 5N)' equal to zero and attempt to solve:

Simplifying
1 + 5N = 0

Solving
1 + 5N = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5N = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5N = 0 + -1
5N = 0 + -1

Combine like terms: 0 + -1 = -1
5N = -1

Divide each side by '5'.
N = -0.2

Simplifying
N = -0.2
Solution
N = {-0.75, -0.2}