4(r-2)-3(r-1)=2(r+3)

Solution for 4(r-2)-3(r-1)=2(r+3) equation:

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

Reorder the terms:
4(-2 + r) + -3(r + -1) = 2(r + 3)
(-2 * 4 + r * 4) + -3(r + -1) = 2(r + 3)
(-8 + 4r) + -3(r + -1) = 2(r + 3)

Reorder the terms:
-8 + 4r + -3(-1 + r) = 2(r + 3)
-8 + 4r + (-1 * -3 + r * -3) = 2(r + 3)
-8 + 4r + (3 + -3r) = 2(r + 3)

Reorder the terms:
-8 + 3 + 4r + -3r = 2(r + 3)

Combine like terms: -8 + 3 = -5
-5 + 4r + -3r = 2(r + 3)

Combine like terms: 4r + -3r = 1r
-5 + 1r = 2(r + 3)

Reorder the terms:
-5 + 1r = 2(3 + r)
-5 + 1r = (3 * 2 + r * 2)
-5 + 1r = (6 + 2r)

Solving
-5 + 1r = 6 + 2r

Solving for variable 'r'.

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

Add '-2r' to each side of the equation.
-5 + 1r + -2r = 6 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-5 + -1r = 6 + 2r + -2r

Combine like terms: 2r + -2r = 0
-5 + -1r = 6 + 0
-5 + -1r = 6

Add '5' to each side of the equation.
-5 + 5 + -1r = 6 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 6 + 5
-1r = 6 + 5

Combine like terms: 6 + 5 = 11
-1r = 11

Divide each side by '-1'.
r = -11

Simplifying
r = -11