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

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

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

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

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

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

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

Solving
5 + -11x + 2x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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