r-3=3r(r-3)

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

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

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

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

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

Solving for variable 'r'.

Combine like terms: r + 9r = 10r
-3 + 10r + -3r2 = -9r + 3r2 + 9r + -3r2

Reorder the terms:
-3 + 10r + -3r2 = -9r + 9r + 3r2 + -3r2

Combine like terms: -9r + 9r = 0
-3 + 10r + -3r2 = 0 + 3r2 + -3r2
-3 + 10r + -3r2 = 3r2 + -3r2

Combine like terms: 3r2 + -3r2 = 0
-3 + 10r + -3r2 = 0

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

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

Simplifying
-3 + r = 0

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

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

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

Simplifying
r = 3
Subproblem 2
Set the factor '(1 + -3r)' equal to zero and attempt to solve:

Simplifying
1 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 0.3333333333

Simplifying
r = 0.3333333333
Solution
r = {3, 0.3333333333}