15r-75+5r-25=3r^2-15r

Solution for 15r-75+5r-25=3r^2-15r equation:

Simplifying
15r + -75 + 5r + -25 = 3r2 + -15r

Reorder the terms:
-75 + -25 + 15r + 5r = 3r2 + -15r

Combine like terms: -75 + -25 = -100
-100 + 15r + 5r = 3r2 + -15r

Combine like terms: 15r + 5r = 20r
-100 + 20r = 3r2 + -15r

Reorder the terms:
-100 + 20r = -15r + 3r2

Solving
-100 + 20r = -15r + 3r2

Solving for variable 'r'.

Combine like terms: 20r + 15r = 35r
-100 + 35r + -3r2 = -15r + 3r2 + 15r + -3r2

Reorder the terms:
-100 + 35r + -3r2 = -15r + 15r + 3r2 + -3r2

Combine like terms: -15r + 15r = 0
-100 + 35r + -3r2 = 0 + 3r2 + -3r2
-100 + 35r + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
-100 + 35r + -3r2 = 0

Factor a trinomial.
(-20 + 3r)(5 + -1r) = 0

Subproblem 1
Set the factor '(-20 + 3r)' equal to zero and attempt to solve:

Simplifying
-20 + 3r = 0

Solving
-20 + 3r = 0

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

Add '20' to each side of the equation.
-20 + 20 + 3r = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3r = 0 + 20
3r = 0 + 20

Combine like terms: 0 + 20 = 20
3r = 20

Divide each side by '3'.
r = 6.666666667

Simplifying
r = 6.666666667
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 = {6.666666667, 5}