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

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

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

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

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

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

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

Solving
0 = 5 + -11x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + 11x + -2x2 = 5 + -11x + 2x2 + -5 + 11x + -2x2

Reorder the terms:
-5 + 11x + -2x2 = 5 + -5 + -11x + 11x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-5 + 11x + -2x2 = 0 + -11x + 11x + 2x2 + -2x2
-5 + 11x + -2x2 = -11x + 11x + 2x2 + -2x2

Combine like terms: -11x + 11x = 0
-5 + 11x + -2x2 = 0 + 2x2 + -2x2
-5 + 11x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-5 + 11x + -2x2 = 0

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}