x(x-1)=462

Solution for x(x-1)=462 equation:

Simplifying
x(x + -1) = 462

Reorder the terms:
x(-1 + x) = 462
(-1 * x + x * x) = 462
(-1x + x2) = 462

Solving
-1x + x2 = 462

Solving for variable 'x'.

Reorder the terms:
-462 + -1x + x2 = 462 + -462

Combine like terms: 462 + -462 = 0
-462 + -1x + x2 = 0

Factor a trinomial.
(-21 + -1x)(22 + -1x) = 0

Subproblem 1
Set the factor '(-21 + -1x)' equal to zero and attempt to solve:

Simplifying
-21 + -1x = 0

Solving
-21 + -1x = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1x = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1x = 0 + 21
-1x = 0 + 21

Combine like terms: 0 + 21 = 21
-1x = 21

Divide each side by '-1'.
x = -21

Simplifying
x = -21
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 = {-21, 22}