a(b-c)+b(c-a)=

Solution for a(b-c)+b(c-a)= equation:

Simplifying
a(b + -1c) + b(c + -1a) = 0
(b * a + -1c * a) + b(c + -1a) = 0
(ab + -1ac) + b(c + -1a) = 0

Reorder the terms:
ab + -1ac + b(-1a + c) = 0
ab + -1ac + (-1a * b + c * b) = 0
ab + -1ac + (-1ab + bc) = 0

Reorder the terms:
ab + -1ab + -1ac + bc = 0

Combine like terms: ab + -1ab = 0
0 + -1ac + bc = 0
-1ac + bc = 0

Solving
-1ac + bc = 0

Solving for variable 'a'.

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

Add '-1bc' to each side of the equation.
-1ac + bc + -1bc = 0 + -1bc

Combine like terms: bc + -1bc = 0
-1ac + 0 = 0 + -1bc
-1ac = 0 + -1bc
Remove the zero:
-1ac = -1bc

Divide each side by '-1c'.
a = b

Simplifying
a = b