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

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

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

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

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

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

Combine like terms: -5r + -3r = -8r
(15 + -8r + r2) = 3r(r + -3)

Reorder the terms:
15 + -8r + r2 = 3r(-3 + r)
15 + -8r + r2 = (-3 * 3r + r * 3r)
15 + -8r + r2 = (-9r + 3r2)

Solving
15 + -8r + r2 = -9r + 3r2

Solving for variable 'r'.

Reorder the terms:
15 + -8r + 9r + r2 + -3r2 = -9r + 3r2 + 9r + -3r2

Combine like terms: -8r + 9r = 1r
15 + 1r + r2 + -3r2 = -9r + 3r2 + 9r + -3r2

Combine like terms: r2 + -3r2 = -2r2
15 + 1r + -2r2 = -9r + 3r2 + 9r + -3r2

Reorder the terms:
15 + 1r + -2r2 = -9r + 9r + 3r2 + -3r2

Combine like terms: -9r + 9r = 0
15 + 1r + -2r2 = 0 + 3r2 + -3r2
15 + 1r + -2r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
15 + 1r + -2r2 = 0

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

Subproblem 1
Set the factor '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 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 + -1r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r = 0 + -3
-1r = 0 + -3

Combine like terms: 0 + -3 = -3
-1r = -3

Divide each side by '-1'.
r = 3

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

Simplifying
5 + 2r = 0

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

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

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

Divide each side by '2'.
r = -2.5

Simplifying
r = -2.5
Solution
r = {3, -2.5}