(4r-5)(2r-3)=

Solution for (4r-5)(2r-3)= equation:

Simplifying
(4r + -5)(2r + -3) = 0

Reorder the terms:
(-5 + 4r)(2r + -3) = 0

Reorder the terms:
(-5 + 4r)(-3 + 2r) = 0

Multiply (-5 + 4r) * (-3 + 2r)
(-5(-3 + 2r) + 4r * (-3 + 2r)) = 0
((-3 * -5 + 2r * -5) + 4r * (-3 + 2r)) = 0
((15 + -10r) + 4r * (-3 + 2r)) = 0
(15 + -10r + (-3 * 4r + 2r * 4r)) = 0
(15 + -10r + (-12r + 8r2)) = 0

Combine like terms: -10r + -12r = -22r
(15 + -22r + 8r2) = 0

Solving
15 + -22r + 8r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5 + -4r)(3 + -2r) = 0

Subproblem 1
Set the factor '(5 + -4r)' equal to zero and attempt to solve:

Simplifying
5 + -4r = 0

Solving
5 + -4r = 0

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

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

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

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

Divide each side by '-4'.
r = 1.25

Simplifying
r = 1.25
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 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 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {1.25, 1.5}