(2r-1)(r-2)=0

Solution for (2r-1)(r-2)=0 equation:

Simplifying
(2r + -1)(r + -2) = 0

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

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

Multiply (-1 + 2r) * (-2 + r)
(-1(-2 + r) + 2r * (-2 + r)) = 0
((-2 * -1 + r * -1) + 2r * (-2 + r)) = 0
((2 + -1r) + 2r * (-2 + r)) = 0
(2 + -1r + (-2 * 2r + r * 2r)) = 0
(2 + -1r + (-4r + 2r2)) = 0

Combine like terms: -1r + -4r = -5r
(2 + -5r + 2r2) = 0

Solving
2 + -5r + 2r2 = 0

Solving for variable 'r'.

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

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

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

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

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

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

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

Simplifying
r = 0.5
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {0.5, 2}