x(x-1)=272

Solution for x(x-1)=272 equation:

Simplifying
x(x + -1) = 272

Reorder the terms:
x(-1 + x) = 272
(-1 * x + x * x) = 272
(-1x + x2) = 272

Solving
-1x + x2 = 272

Solving for variable 'x'.

Reorder the terms:
-272 + -1x + x2 = 272 + -272

Combine like terms: 272 + -272 = 0
-272 + -1x + x2 = 0

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

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

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

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

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

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

Simplifying
x = -16
Subproblem 2
Set the factor '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

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

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

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

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

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