(x-21)(x-2)=0

Solution for (x-21)(x-2)=0 equation:

Simplifying
(x + -21)(x + -2) = 0

Reorder the terms:
(-21 + x)(x + -2) = 0

Reorder the terms:
(-21 + x)(-2 + x) = 0

Multiply (-21 + x) * (-2 + x)
(-21(-2 + x) + x(-2 + x)) = 0
((-2 * -21 + x * -21) + x(-2 + x)) = 0
((42 + -21x) + x(-2 + x)) = 0
(42 + -21x + (-2 * x + x * x)) = 0
(42 + -21x + (-2x + x2)) = 0

Combine like terms: -21x + -2x = -23x
(42 + -23x + x2) = 0

Solving
42 + -23x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(21 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
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 = {2, 21}