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

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

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

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

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

Multiply (-1 + 2x) * (-5 + x)
(-1(-5 + x) + 2x * (-5 + x)) = 0
((-5 * -1 + x * -1) + 2x * (-5 + x)) = 0
((5 + -1x) + 2x * (-5 + x)) = 0
(5 + -1x + (-5 * 2x + x * 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.
(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}