(x-2)(4-x)=0

Solution for (x-2)(4-x)=0 equation:

Simplifying
(x + -2)(4 + -1x) = 0

Reorder the terms:
(-2 + x)(4 + -1x) = 0

Multiply (-2 + x) * (4 + -1x)
(-2(4 + -1x) + x(4 + -1x)) = 0
((4 * -2 + -1x * -2) + x(4 + -1x)) = 0
((-8 + 2x) + x(4 + -1x)) = 0
(-8 + 2x + (4 * x + -1x * x)) = 0
(-8 + 2x + (4x + -1x2)) = 0

Combine like terms: 2x + 4x = 6x
(-8 + 6x + -1x2) = 0

Solving
-8 + 6x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 0

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

Add '4' to each side of the equation.
-4 + 4 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4
Subproblem 2
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
Solution
x = {4, 2}