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

Solution for 2(r-2)+3(4r-1)=0 equation:

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

Reorder the terms:
2(-2 + r) + 3(4r + -1) = 0
(-2 * 2 + r * 2) + 3(4r + -1) = 0
(-4 + 2r) + 3(4r + -1) = 0

Reorder the terms:
-4 + 2r + 3(-1 + 4r) = 0
-4 + 2r + (-1 * 3 + 4r * 3) = 0
-4 + 2r + (-3 + 12r) = 0

Reorder the terms:
-4 + -3 + 2r + 12r = 0

Combine like terms: -4 + -3 = -7
-7 + 2r + 12r = 0

Combine like terms: 2r + 12r = 14r
-7 + 14r = 0

Solving
-7 + 14r = 0

Solving for variable 'r'.

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

Add '7' to each side of the equation.
-7 + 7 + 14r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 14r = 0 + 7
14r = 0 + 7

Combine like terms: 0 + 7 = 7
14r = 7

Divide each side by '14'.
r = 0.5

Simplifying
r = 0.5