7(r-5)-6(r-1)=2(r+6)

Solution for 7(r-5)-6(r-1)=2(r+6) equation:

Simplifying
7(r + -5) + -6(r + -1) = 2(r + 6)

Reorder the terms:
7(-5 + r) + -6(r + -1) = 2(r + 6)
(-5 * 7 + r * 7) + -6(r + -1) = 2(r + 6)
(-35 + 7r) + -6(r + -1) = 2(r + 6)

Reorder the terms:
-35 + 7r + -6(-1 + r) = 2(r + 6)
-35 + 7r + (-1 * -6 + r * -6) = 2(r + 6)
-35 + 7r + (6 + -6r) = 2(r + 6)

Reorder the terms:
-35 + 6 + 7r + -6r = 2(r + 6)

Combine like terms: -35 + 6 = -29
-29 + 7r + -6r = 2(r + 6)

Combine like terms: 7r + -6r = 1r
-29 + 1r = 2(r + 6)

Reorder the terms:
-29 + 1r = 2(6 + r)
-29 + 1r = (6 * 2 + r * 2)
-29 + 1r = (12 + 2r)

Solving
-29 + 1r = 12 + 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.
-29 + 1r + -2r = 12 + 2r + -2r

Combine like terms: 1r + -2r = -1r
-29 + -1r = 12 + 2r + -2r

Combine like terms: 2r + -2r = 0
-29 + -1r = 12 + 0
-29 + -1r = 12

Add '29' to each side of the equation.
-29 + 29 + -1r = 12 + 29

Combine like terms: -29 + 29 = 0
0 + -1r = 12 + 29
-1r = 12 + 29

Combine like terms: 12 + 29 = 41
-1r = 41

Divide each side by '-1'.
r = -41

Simplifying
r = -41