2(r-3)=3(r-4)

Solution for 2(r-3)=3(r-4) equation:

Simplifying
2(r + -3) = 3(r + -4)

Reorder the terms:
2(-3 + r) = 3(r + -4)
(-3 * 2 + r * 2) = 3(r + -4)
(-6 + 2r) = 3(r + -4)

Reorder the terms:
-6 + 2r = 3(-4 + r)
-6 + 2r = (-4 * 3 + r * 3)
-6 + 2r = (-12 + 3r)

Solving
-6 + 2r = -12 + 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 = -12 + 3r + -3r

Combine like terms: 2r + -3r = -1r
-6 + -1r = -12 + 3r + -3r

Combine like terms: 3r + -3r = 0
-6 + -1r = -12 + 0
-6 + -1r = -12

Add '6' to each side of the equation.
-6 + 6 + -1r = -12 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = -12 + 6
-1r = -12 + 6

Combine like terms: -12 + 6 = -6
-1r = -6

Divide each side by '-1'.
r = 6

Simplifying
r = 6