n(n-1)=136*2

Solution for n(n-1)=136*2 equation:

Simplifying
n(n + -1) = 136 * 2

Reorder the terms:
n(-1 + n) = 136 * 2
(-1 * n + n * n) = 136 * 2
(-1n + n2) = 136 * 2

Multiply 136 * 2
-1n + n2 = 272

Solving
-1n + n2 = 272

Solving for variable 'n'.

Reorder the terms:
-272 + -1n + n2 = 272 + -272

Combine like terms: 272 + -272 = 0
-272 + -1n + n2 = 0

Factor a trinomial.
(-16 + -1n)(17 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(17 + -1n)' equal to zero and attempt to solve:

Simplifying
17 + -1n = 0

Solving
17 + -1n = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1n = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1n = 0 + -17
-1n = 0 + -17

Combine like terms: 0 + -17 = -17
-1n = -17

Divide each side by '-1'.
n = 17

Simplifying
n = 17
Solution
n = {-16, 17}