(30-1x)(420-10x)=0

Solution for (30-1x)(420-10x)=0 equation:

Simplifying
(30 + -1x)(420 + -10x) = 0

Multiply (30 + -1x) * (420 + -10x)
(30(420 + -10x) + -1x * (420 + -10x)) = 0
((420 * 30 + -10x * 30) + -1x * (420 + -10x)) = 0
((12600 + -300x) + -1x * (420 + -10x)) = 0
(12600 + -300x + (420 * -1x + -10x * -1x)) = 0
(12600 + -300x + (-420x + 10x2)) = 0

Combine like terms: -300x + -420x = -720x
(12600 + -720x + 10x2) = 0

Solving
12600 + -720x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(1260 + -72x + x2) = 0

Factor a trinomial.
10((30 + -1x)(42 + -1x)) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve:

Simplifying
30 + -1x = 0

Solving
30 + -1x = 0

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

Add '-30' to each side of the equation.
30 + -30 + -1x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -1x = 0 + -30
-1x = 0 + -30

Combine like terms: 0 + -30 = -30
-1x = -30

Divide each side by '-1'.
x = 30

Simplifying
x = 30
Subproblem 2
Set the factor '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x = 0 + -42
-1x = 0 + -42

Combine like terms: 0 + -42 = -42
-1x = -42

Divide each side by '-1'.
x = 42

Simplifying
x = 42
Solution
x = {30, 42}