8(r-5)-7(r-1)=2(r+7)

Solution for 8(r-5)-7(r-1)=2(r+7) equation:

Simplifying
8(r + -5) + -7(r + -1) = 2(r + 7)

Reorder the terms:
8(-5 + r) + -7(r + -1) = 2(r + 7)
(-5 * 8 + r * 8) + -7(r + -1) = 2(r + 7)
(-40 + 8r) + -7(r + -1) = 2(r + 7)

Reorder the terms:
-40 + 8r + -7(-1 + r) = 2(r + 7)
-40 + 8r + (-1 * -7 + r * -7) = 2(r + 7)
-40 + 8r + (7 + -7r) = 2(r + 7)

Reorder the terms:
-40 + 7 + 8r + -7r = 2(r + 7)

Combine like terms: -40 + 7 = -33
-33 + 8r + -7r = 2(r + 7)

Combine like terms: 8r + -7r = 1r
-33 + 1r = 2(r + 7)

Reorder the terms:
-33 + 1r = 2(7 + r)
-33 + 1r = (7 * 2 + r * 2)
-33 + 1r = (14 + 2r)

Solving
-33 + 1r = 14 + 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.
-33 + 1r + -2r = 14 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-33 + -1r = 14 + 2r + -2r

Combine like terms: 2r + -2r = 0
-33 + -1r = 14 + 0
-33 + -1r = 14

Add '33' to each side of the equation.
-33 + 33 + -1r = 14 + 33

Combine like terms: -33 + 33 = 0
0 + -1r = 14 + 33
-1r = 14 + 33

Combine like terms: 14 + 33 = 47
-1r = 47

Divide each side by '-1'.
r = -47

Simplifying
r = -47