2(r-4)+4(r-2)=-4(r-1)+11(r+2)

Solution for 2(r-4)+4(r-2)=-4(r-1)+11(r+2) equation:

Simplifying
2(r + -4) + 4(r + -2) = -4(r + -1) + 11(r + 2)

Reorder the terms:
2(-4 + r) + 4(r + -2) = -4(r + -1) + 11(r + 2)
(-4 * 2 + r * 2) + 4(r + -2) = -4(r + -1) + 11(r + 2)
(-8 + 2r) + 4(r + -2) = -4(r + -1) + 11(r + 2)

Reorder the terms:
-8 + 2r + 4(-2 + r) = -4(r + -1) + 11(r + 2)
-8 + 2r + (-2 * 4 + r * 4) = -4(r + -1) + 11(r + 2)
-8 + 2r + (-8 + 4r) = -4(r + -1) + 11(r + 2)

Reorder the terms:
-8 + -8 + 2r + 4r = -4(r + -1) + 11(r + 2)

Combine like terms: -8 + -8 = -16
-16 + 2r + 4r = -4(r + -1) + 11(r + 2)

Combine like terms: 2r + 4r = 6r
-16 + 6r = -4(r + -1) + 11(r + 2)

Reorder the terms:
-16 + 6r = -4(-1 + r) + 11(r + 2)
-16 + 6r = (-1 * -4 + r * -4) + 11(r + 2)
-16 + 6r = (4 + -4r) + 11(r + 2)

Reorder the terms:
-16 + 6r = 4 + -4r + 11(2 + r)
-16 + 6r = 4 + -4r + (2 * 11 + r * 11)
-16 + 6r = 4 + -4r + (22 + 11r)

Reorder the terms:
-16 + 6r = 4 + 22 + -4r + 11r

Combine like terms: 4 + 22 = 26
-16 + 6r = 26 + -4r + 11r

Combine like terms: -4r + 11r = 7r
-16 + 6r = 26 + 7r

Solving
-16 + 6r = 26 + 7r

Solving for variable 'r'.

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

Add '-7r' to each side of the equation.
-16 + 6r + -7r = 26 + 7r + -7r

Combine like terms: 6r + -7r = -1r
-16 + -1r = 26 + 7r + -7r

Combine like terms: 7r + -7r = 0
-16 + -1r = 26 + 0
-16 + -1r = 26

Add '16' to each side of the equation.
-16 + 16 + -1r = 26 + 16

Combine like terms: -16 + 16 = 0
0 + -1r = 26 + 16
-1r = 26 + 16

Combine like terms: 26 + 16 = 42
-1r = 42

Divide each side by '-1'.
r = -42

Simplifying
r = -42