(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.
(-22 + -1x)(23 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-22, 23}