(x-2)(5-x)=0

Solution for (x-2)(5-x)=0 equation:

Simplifying
(x + -2)(5 + -1x) = 0

Reorder the terms:
(-2 + x)(5 + -1x) = 0

Multiply (-2 + x) * (5 + -1x)
(-2(5 + -1x) + x(5 + -1x)) = 0
((5 * -2 + -1x * -2) + x(5 + -1x)) = 0
((-10 + 2x) + x(5 + -1x)) = 0
(-10 + 2x + (5 * x + -1x * x)) = 0
(-10 + 2x + (5x + -1x2)) = 0

Combine like terms: 2x + 5x = 7x
(-10 + 7x + -1x2) = 0

Solving
-10 + 7x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 5
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 = {5, 2}