(2x-1)*(5-x)=0

Solution for (2x-1)*(5-x)=0 equation:

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

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

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

Combine like terms: 1x + 10x = 11x
(-5 + 11x + -2x2) = 0

Solving
-5 + 11x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + x)(1 + -2x) = 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 '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {5, 0.5}