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

Solution for 5(r-2)-4(r-1)=2(r+4) equation:

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

Reorder the terms:
5(-2 + r) + -4(r + -1) = 2(r + 4)
(-2 * 5 + r * 5) + -4(r + -1) = 2(r + 4)
(-10 + 5r) + -4(r + -1) = 2(r + 4)

Reorder the terms:
-10 + 5r + -4(-1 + r) = 2(r + 4)
-10 + 5r + (-1 * -4 + r * -4) = 2(r + 4)
-10 + 5r + (4 + -4r) = 2(r + 4)

Reorder the terms:
-10 + 4 + 5r + -4r = 2(r + 4)

Combine like terms: -10 + 4 = -6
-6 + 5r + -4r = 2(r + 4)

Combine like terms: 5r + -4r = 1r
-6 + 1r = 2(r + 4)

Reorder the terms:
-6 + 1r = 2(4 + r)
-6 + 1r = (4 * 2 + r * 2)
-6 + 1r = (8 + 2r)

Solving
-6 + 1r = 8 + 2r

Solving for variable 'r'.

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

Add '-2r' to each side of the equation.
-6 + 1r + -2r = 8 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-6 + -1r = 8 + 2r + -2r

Combine like terms: 2r + -2r = 0
-6 + -1r = 8 + 0
-6 + -1r = 8

Add '6' to each side of the equation.
-6 + 6 + -1r = 8 + 6

Combine like terms: -6 + 6 = 0
0 + -1r = 8 + 6
-1r = 8 + 6

Combine like terms: 8 + 6 = 14
-1r = 14

Divide each side by '-1'.
r = -14

Simplifying
r = -14