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

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

Simplifying
5r + 2(1 + -1r) = 2(2r + -1)
5r + (1 * 2 + -1r * 2) = 2(2r + -1)
5r + (2 + -2r) = 2(2r + -1)

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

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

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

Solving
2 + 3r = -2 + 4r

Solving for variable 'r'.

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

Add '-4r' to each side of the equation.
2 + 3r + -4r = -2 + 4r + -4r

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

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

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

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

Combine like terms: -2 + -2 = -4
-1r = -4

Divide each side by '-1'.
r = 4

Simplifying
r = 4