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

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

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

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

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

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

Combine like terms: -10r + -2r = -12r
(4 + -12r + 5r2) = 0

Solving
4 + -12r + 5r2 = 0

Solving for variable 'r'.

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

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

Simplifying
2 + -5r = 0

Solving
2 + -5r = 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 + -5r = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5r = 0 + -2
-5r = 0 + -2

Combine like terms: 0 + -2 = -2
-5r = -2

Divide each side by '-5'.
r = 0.4

Simplifying
r = 0.4
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 = {0.4, 2}