=(N+4)(N-5)

Solution for =(N+4)(N-5) equation:

Simplifying
0 = (N + 4)(N + -5)

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

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

Multiply (4 + N) * (-5 + N)
0 = (4(-5 + N) + N(-5 + N))
0 = ((-5 * 4 + N * 4) + N(-5 + N))
0 = ((-20 + 4N) + N(-5 + N))
0 = (-20 + 4N + (-5 * N + N * N))
0 = (-20 + 4N + (-5N + N2))

Combine like terms: 4N + -5N = -1N
0 = (-20 + -1N + N2)

Solving
0 = -20 + -1N + N2

Solving for variable 'N'.

Combine like terms: 0 + 20 = 20
20 + N + -1N2 = -20 + -1N + N2 + 20 + N + -1N2

Reorder the terms:
20 + N + -1N2 = -20 + 20 + -1N + N + N2 + -1N2

Combine like terms: -20 + 20 = 0
20 + N + -1N2 = 0 + -1N + N + N2 + -1N2
20 + N + -1N2 = -1N + N + N2 + -1N2

Combine like terms: -1N + N = 0
20 + N + -1N2 = 0 + N2 + -1N2
20 + N + -1N2 = N2 + -1N2

Combine like terms: N2 + -1N2 = 0
20 + N + -1N2 = 0

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

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

Simplifying
5 + -1N = 0

Solving
5 + -1N = 0

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

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

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

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

Divide each side by '-1'.
N = 5

Simplifying
N = 5
Subproblem 2
Set the factor '(4 + N)' equal to zero and attempt to solve:

Simplifying
4 + N = 0

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

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

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

Simplifying
N = -4
Solution
N = {5, -4}