(4r-1)(5r-3)=

Solution for (4r-1)(5r-3)= equation:

Simplifying
(4r + -1)(5r + -3) = 0

Reorder the terms:
(-1 + 4r)(5r + -3) = 0

Reorder the terms:
(-1 + 4r)(-3 + 5r) = 0

Multiply (-1 + 4r) * (-3 + 5r)
(-1(-3 + 5r) + 4r * (-3 + 5r)) = 0
((-3 * -1 + 5r * -1) + 4r * (-3 + 5r)) = 0
((3 + -5r) + 4r * (-3 + 5r)) = 0
(3 + -5r + (-3 * 4r + 5r * 4r)) = 0
(3 + -5r + (-12r + 20r2)) = 0

Combine like terms: -5r + -12r = -17r
(3 + -17r + 20r2) = 0

Solving
3 + -17r + 20r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(1 + -4r)(3 + -5r) = 0

Subproblem 1
Set the factor '(1 + -4r)' equal to zero and attempt to solve:

Simplifying
1 + -4r = 0

Solving
1 + -4r = 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 + -4r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4r = 0 + -1
-4r = 0 + -1

Combine like terms: 0 + -1 = -1
-4r = -1

Divide each side by '-4'.
r = 0.25

Simplifying
r = 0.25
Subproblem 2
Set the factor '(3 + -5r)' equal to zero and attempt to solve:

Simplifying
3 + -5r = 0

Solving
3 + -5r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5r = 0 + -3
-5r = 0 + -3

Combine like terms: 0 + -3 = -3
-5r = -3

Divide each side by '-5'.
r = 0.6

Simplifying
r = 0.6
Solution
r = {0.25, 0.6}