2r-2(r+3)=4[2r-3(1+r)]

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

Simplifying
2r + -2(r + 3) = 4[2r + -3(1 + r)]

Reorder the terms:
2r + -2(3 + r) = 4[2r + -3(1 + r)]
2r + (3 * -2 + r * -2) = 4[2r + -3(1 + r)]
2r + (-6 + -2r) = 4[2r + -3(1 + r)]

Reorder the terms:
-6 + 2r + -2r = 4[2r + -3(1 + r)]

Combine like terms: 2r + -2r = 0
-6 + 0 = 4[2r + -3(1 + r)]
-6 = 4[2r + -3(1 + r)]
-6 = 4[2r + (1 * -3 + r * -3)]
-6 = 4[2r + (-3 + -3r)]

Reorder the terms:
-6 = 4[-3 + 2r + -3r]

Combine like terms: 2r + -3r = -1r
-6 = 4[-3 + -1r]
-6 = [-3 * 4 + -1r * 4]
-6 = [-12 + -4r]

Solving
-6 = -12 + -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.
-6 + 4r = -12 + -4r + 4r

Combine like terms: -4r + 4r = 0
-6 + 4r = -12 + 0
-6 + 4r = -12

Add '6' to each side of the equation.
-6 + 6 + 4r = -12 + 6

Combine like terms: -6 + 6 = 0
0 + 4r = -12 + 6
4r = -12 + 6

Combine like terms: -12 + 6 = -6
4r = -6

Divide each side by '4'.
r = -1.5

Simplifying
r = -1.5