x(x-1)=420

Solution for x(x-1)=420 equation:

Simplifying
x(x + -1) = 420

Reorder the terms:
x(-1 + x) = 420
(-1 * x + x * x) = 420
(-1x + x2) = 420

Solving
-1x + x2 = 420

Solving for variable 'x'.

Reorder the terms:
-420 + -1x + x2 = 420 + -420

Combine like terms: 420 + -420 = 0
-420 + -1x + x2 = 0

Factor a trinomial.
(-20 + -1x)(21 + -1x) = 0

Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve:

Simplifying
-20 + -1x = 0

Solving
-20 + -1x = 0

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

Add '20' to each side of the equation.
-20 + 20 + -1x = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -1x = 0 + 20
-1x = 0 + 20

Combine like terms: 0 + 20 = 20
-1x = 20

Divide each side by '-1'.
x = -20

Simplifying
x = -20
Subproblem 2
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
Solution
x = {-20, 21}