(4r-2)(5r-4)=0

Solution for (4r-2)(5r-4)=0 equation:

Simplifying
(4r + -2)(5r + -4) = 0

Reorder the terms:
(-2 + 4r)(5r + -4) = 0

Reorder the terms:
(-2 + 4r)(-4 + 5r) = 0

Multiply (-2 + 4r) * (-4 + 5r)
(-2(-4 + 5r) + 4r * (-4 + 5r)) = 0
((-4 * -2 + 5r * -2) + 4r * (-4 + 5r)) = 0
((8 + -10r) + 4r * (-4 + 5r)) = 0
(8 + -10r + (-4 * 4r + 5r * 4r)) = 0
(8 + -10r + (-16r + 20r2)) = 0

Combine like terms: -10r + -16r = -26r
(8 + -26r + 20r2) = 0

Solving
8 + -26r + 20r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + -13r + 10r2) = 0

Factor a trinomial.
2((1 + -2r)(4 + -5r)) = 0

Ignore the factor 2.
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 '(4 + -5r)' equal to zero and attempt to solve:

Simplifying
4 + -5r = 0

Solving
4 + -5r = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5r = 0 + -4
-5r = 0 + -4

Combine like terms: 0 + -4 = -4
-5r = -4

Divide each side by '-5'.
r = 0.8

Simplifying
r = 0.8
Solution
r = {0.5, 0.8}