x(x+1)=506

Solution for x(x+1)=506 equation:

Simplifying
x(x + 1) = 506

Reorder the terms:
x(1 + x) = 506
(1 * x + x * x) = 506
(1x + x2) = 506

Solving
1x + x2 = 506

Solving for variable 'x'.

Reorder the terms:
-506 + 1x + x2 = 506 + -506

Combine like terms: 506 + -506 = 0
-506 + 1x + x2 = 0

Factor a trinomial.
(-23 + -1x)(22 + -1x) = 0

Subproblem 1
Set the factor '(-23 + -1x)' equal to zero and attempt to solve:

Simplifying
-23 + -1x = 0

Solving
-23 + -1x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -1x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -1x = 0 + 23
-1x = 0 + 23

Combine like terms: 0 + 23 = 23
-1x = 23

Divide each side by '-1'.
x = -23

Simplifying
x = -23
Subproblem 2
Set the factor '(22 + -1x)' equal to zero and attempt to solve:

Simplifying
22 + -1x = 0

Solving
22 + -1x = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1x = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1x = 0 + -22
-1x = 0 + -22

Combine like terms: 0 + -22 = -22
-1x = -22

Divide each side by '-1'.
x = 22

Simplifying
x = 22
Solution
x = {-23, 22}