-2(c-d)+(c-d)-6(c-d)=0

Solution for -2(c-d)+(c-d)-6(c-d)=0 equation:

Simplifying
-2(c + -1d) + (c + -1d) + -6(c + -1d) = 0
(c * -2 + -1d * -2) + (c + -1d) + -6(c + -1d) = 0
(-2c + 2d) + (c + -1d) + -6(c + -1d) = 0

Remove parenthesis around (c + -1d)
-2c + 2d + c + -1d + -6(c + -1d) = 0
-2c + 2d + c + -1d + (c * -6 + -1d * -6) = 0
-2c + 2d + c + -1d + (-6c + 6d) = 0

Reorder the terms:
-2c + c + -6c + 2d + -1d + 6d = 0

Combine like terms: -2c + c = -1c
-1c + -6c + 2d + -1d + 6d = 0

Combine like terms: -1c + -6c = -7c
-7c + 2d + -1d + 6d = 0

Combine like terms: 2d + -1d = 1d
-7c + 1d + 6d = 0

Combine like terms: 1d + 6d = 7d
-7c + 7d = 0

Solving
-7c + 7d = 0

Solving for variable 'c'.

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

Add '-7d' to each side of the equation.
-7c + 7d + -7d = 0 + -7d

Combine like terms: 7d + -7d = 0
-7c + 0 = 0 + -7d
-7c = 0 + -7d
Remove the zero:
-7c = -7d

Divide each side by '-7'.
c = d

Simplifying
c = d