2r-6=3(3-r)

Solution for 2r-6=3(3-r) equation:

Simplifying
2r + -6 = 3(3 + -1r)

Reorder the terms:
-6 + 2r = 3(3 + -1r)
-6 + 2r = (3 * 3 + -1r * 3)
-6 + 2r = (9 + -3r)

Solving
-6 + 2r = 9 + -3r

Solving for variable 'r'.

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

Add '3r' to each side of the equation.
-6 + 2r + 3r = 9 + -3r + 3r

Combine like terms: 2r + 3r = 5r
-6 + 5r = 9 + -3r + 3r

Combine like terms: -3r + 3r = 0
-6 + 5r = 9 + 0
-6 + 5r = 9

Add '6' to each side of the equation.
-6 + 6 + 5r = 9 + 6

Combine like terms: -6 + 6 = 0
0 + 5r = 9 + 6
5r = 9 + 6

Combine like terms: 9 + 6 = 15
5r = 15

Divide each side by '5'.
r = 3

Simplifying
r = 3