2(3r-s)=5(s+2t)-4(2t+s)

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

Simplifying
2(3r + -1s) = 5(s + 2t) + -4(2t + s)
(3r * 2 + -1s * 2) = 5(s + 2t) + -4(2t + s)
(6r + -2s) = 5(s + 2t) + -4(2t + s)
6r + -2s = (s * 5 + 2t * 5) + -4(2t + s)
6r + -2s = (5s + 10t) + -4(2t + s)

Reorder the terms:
6r + -2s = 5s + 10t + -4(s + 2t)
6r + -2s = 5s + 10t + (s * -4 + 2t * -4)
6r + -2s = 5s + 10t + (-4s + -8t)

Reorder the terms:
6r + -2s = 5s + -4s + 10t + -8t

Combine like terms: 5s + -4s = 1s
6r + -2s = 1s + 10t + -8t

Combine like terms: 10t + -8t = 2t
6r + -2s = 1s + 2t

Solving
6r + -2s = 1s + 2t

Solving for variable 'r'.

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

Add '2s' to each side of the equation.
6r + -2s + 2s = 1s + 2s + 2t

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

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

Divide each side by '6'.
r = 0.5s + 0.3333333333t

Simplifying
r = 0.5s + 0.3333333333t