(z-6)+[-(z-6)]=0

Solution for (z-6)+[-(z-6)]=0 equation:

Simplifying
(z + -6) + [-1(z + -6)] = 0

Reorder the terms:
(-6 + z) + [-1(z + -6)] = 0

Remove parenthesis around (-6 + z)
-6 + z + [-1(z + -6)] = 0

Reorder the terms:
-6 + z + [-1(-6 + z)] = 0
-6 + z + [(-6 * -1 + z * -1)] = 0
-6 + z + [(6 + -1z)] = 0
-6 + z + [6 + -1z] = 0

Remove brackets around [6 + -1z]
-6 + z + 6 + -1z = 0

Reorder the terms:
-6 + 6 + z + -1z = 0

Combine like terms: -6 + 6 = 0
0 + z + -1z = 0
z + -1z = 0

Combine like terms: z + -1z = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.