.5r+2(.75r+1)=.25r+6

Solution for .5r+2(.75r+1)=.25r+6 equation:

Simplifying
0.5r + 2(0.75r + 1) = 0.25r + 6

Reorder the terms:
0.5r + 2(1 + 0.75r) = 0.25r + 6
0.5r + (1 * 2 + 0.75r * 2) = 0.25r + 6
0.5r + (2 + 1.5r) = 0.25r + 6

Reorder the terms:
2 + 0.5r + 1.5r = 0.25r + 6

Combine like terms: 0.5r + 1.5r = 2r
2 + 2r = 0.25r + 6

Reorder the terms:
2 + 2r = 6 + 0.25r

Solving
2 + 2r = 6 + 0.25r

Solving for variable 'r'.

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

Add '-0.25r' to each side of the equation.
2 + 2r + -0.25r = 6 + 0.25r + -0.25r

Combine like terms: 2r + -0.25r = 1.75r
2 + 1.75r = 6 + 0.25r + -0.25r

Combine like terms: 0.25r + -0.25r = 0.00
2 + 1.75r = 6 + 0.00
2 + 1.75r = 6

Add '-2' to each side of the equation.
2 + -2 + 1.75r = 6 + -2

Combine like terms: 2 + -2 = 0
0 + 1.75r = 6 + -2
1.75r = 6 + -2

Combine like terms: 6 + -2 = 4
1.75r = 4

Divide each side by '1.75'.
r = 2.285714286

Simplifying
r = 2.285714286