4(r-3)-3(r-1)=2(r+5)

Solution for 4(r-3)-3(r-1)=2(r+5) equation:

Simplifying
4(r + -3) + -3(r + -1) = 2(r + 5)

Reorder the terms:
4(-3 + r) + -3(r + -1) = 2(r + 5)
(-3 * 4 + r * 4) + -3(r + -1) = 2(r + 5)
(-12 + 4r) + -3(r + -1) = 2(r + 5)

Reorder the terms:
-12 + 4r + -3(-1 + r) = 2(r + 5)
-12 + 4r + (-1 * -3 + r * -3) = 2(r + 5)
-12 + 4r + (3 + -3r) = 2(r + 5)

Reorder the terms:
-12 + 3 + 4r + -3r = 2(r + 5)

Combine like terms: -12 + 3 = -9
-9 + 4r + -3r = 2(r + 5)

Combine like terms: 4r + -3r = 1r
-9 + 1r = 2(r + 5)

Reorder the terms:
-9 + 1r = 2(5 + r)
-9 + 1r = (5 * 2 + r * 2)
-9 + 1r = (10 + 2r)

Solving
-9 + 1r = 10 + 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.
-9 + 1r + -2r = 10 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-9 + -1r = 10 + 2r + -2r

Combine like terms: 2r + -2r = 0
-9 + -1r = 10 + 0
-9 + -1r = 10

Add '9' to each side of the equation.
-9 + 9 + -1r = 10 + 9

Combine like terms: -9 + 9 = 0
0 + -1r = 10 + 9
-1r = 10 + 9

Combine like terms: 10 + 9 = 19
-1r = 19

Divide each side by '-1'.
r = -19

Simplifying
r = -19