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.
(-17 + -1x)(16 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-17, 16}