420=(10)(x-1)(x)

Solution for 420=(10)(x-1)(x) equation:

Simplifying
420 = (10)(x + -1)(x)

Reorder the terms:
420 = 10(-1 + x)(x)

Reorder the terms for easier multiplication:
420 = 10x(-1 + x)
420 = (-1 * 10x + x * 10x)
420 = (-10x + 10x2)

Solving
420 = -10x + 10x2

Solving for variable 'x'.

Reorder the terms:
420 + 10x + -10x2 = -10x + 10x + 10x2 + -10x2

Combine like terms: -10x + 10x = 0
420 + 10x + -10x2 = 0 + 10x2 + -10x2
420 + 10x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
420 + 10x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(42 + x + -1x2) = 0

Factor a trinomial.
10((7 + -1x)(6 + x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {7, -6}