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

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

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

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

Reorder the terms:
6 + 2r = 6(-3 + r)
6 + 2r = (-3 * 6 + r * 6)
6 + 2r = (-18 + 6r)

Solving
6 + 2r = -18 + 6r

Solving for variable 'r'.

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

Add '-6r' to each side of the equation.
6 + 2r + -6r = -18 + 6r + -6r

Combine like terms: 2r + -6r = -4r
6 + -4r = -18 + 6r + -6r

Combine like terms: 6r + -6r = 0
6 + -4r = -18 + 0
6 + -4r = -18

Add '-6' to each side of the equation.
6 + -6 + -4r = -18 + -6

Combine like terms: 6 + -6 = 0
0 + -4r = -18 + -6
-4r = -18 + -6

Combine like terms: -18 + -6 = -24
-4r = -24

Divide each side by '-4'.
r = 6

Simplifying
r = 6