N(N-24)=-128

Solution for N(N-24)=-128 equation:

Simplifying
N(N + -24) = -128

Reorder the terms:
N(-24 + N) = -128
(-24 * N + N * N) = -128
(-24N + N2) = -128

Solving
-24N + N2 = -128

Solving for variable 'N'.

Reorder the terms:
128 + -24N + N2 = -128 + 128

Combine like terms: -128 + 128 = 0
128 + -24N + N2 = 0

Factor a trinomial.
(8 + -1N)(16 + -1N) = 0

Subproblem 1
Set the factor '(8 + -1N)' equal to zero and attempt to solve:

Simplifying
8 + -1N = 0

Solving
8 + -1N = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1N = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1N = 0 + -8
-1N = 0 + -8

Combine like terms: 0 + -8 = -8
-1N = -8

Divide each side by '-1'.
N = 8

Simplifying
N = 8
Subproblem 2
Set the factor '(16 + -1N)' equal to zero and attempt to solve:

Simplifying
16 + -1N = 0

Solving
16 + -1N = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1N = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1N = 0 + -16
-1N = 0 + -16

Combine like terms: 0 + -16 = -16
-1N = -16

Divide each side by '-1'.
N = 16

Simplifying
N = 16
Solution
N = {8, 16}