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

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

Simplifying
(4r + -1s) + -1(r + 2s) + (3r + -1s) = 0

Remove parenthesis around (4r + -1s)
4r + -1s + -1(r + 2s) + (3r + -1s) = 0
4r + -1s + (r * -1 + 2s * -1) + (3r + -1s) = 0
4r + -1s + (-1r + -2s) + (3r + -1s) = 0

Remove parenthesis around (3r + -1s)
4r + -1s + -1r + -2s + 3r + -1s = 0

Reorder the terms:
4r + -1r + 3r + -1s + -2s + -1s = 0

Combine like terms: 4r + -1r = 3r
3r + 3r + -1s + -2s + -1s = 0

Combine like terms: 3r + 3r = 6r
6r + -1s + -2s + -1s = 0

Combine like terms: -1s + -2s = -3s
6r + -3s + -1s = 0

Combine like terms: -3s + -1s = -4s
6r + -4s = 0

Solving
6r + -4s = 0

Solving for variable 'r'.

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

Add '4s' to each side of the equation.
6r + -4s + 4s = 0 + 4s

Combine like terms: -4s + 4s = 0
6r + 0 = 0 + 4s
6r = 0 + 4s
Remove the zero:
6r = 4s

Divide each side by '6'.
r = 0.6666666667s

Simplifying
r = 0.6666666667s