420=x(x-1)

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

Simplifying
420 = x(x + -1)

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

Solving
420 = -1x + x2

Solving for variable 'x'.

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

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

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

Factor a trinomial.
(21 + -1x)(20 + x) = 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 '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 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 + x = 0 + -20

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

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

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