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

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

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

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

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

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

Combine like terms: -10r + -3r = -13r
(15 + -13r + 2r2) = 0

Solving
15 + -13r + 2r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3 + -2r)(5 + -1r) = 0

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

Simplifying
5 + -1r = 0

Solving
5 + -1r = 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 + -1r = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r = 0 + -5
-1r = 0 + -5

Combine like terms: 0 + -5 = -5
-1r = -5

Divide each side by '-1'.
r = 5

Simplifying
r = 5
Solution
r = {1.5, 5}