a(b-2)+c(b-2)=0

Solution for a(b-2)+c(b-2)=0 equation:

Simplifying
a(b + -2) + c(b + -2) = 0

Reorder the terms:
a(-2 + b) + c(b + -2) = 0
(-2 * a + b * a) + c(b + -2) = 0
(-2a + ab) + c(b + -2) = 0

Reorder the terms:
-2a + ab + c(-2 + b) = 0
-2a + ab + (-2 * c + b * c) = 0

Reorder the terms:
-2a + ab + (bc + -2c) = 0
-2a + ab + (bc + -2c) = 0

Solving
-2a + ab + bc + -2c = 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.
-2a + ab + bc + -1bc + -2c = 0 + -1bc

Combine like terms: bc + -1bc = 0
-2a + ab + 0 + -2c = 0 + -1bc
-2a + ab + -2c = 0 + -1bc
Remove the zero:
-2a + ab + -2c = -1bc

Add '2c' to each side of the equation.
-2a + ab + -2c + 2c = -1bc + 2c

Combine like terms: -2c + 2c = 0
-2a + ab + 0 = -1bc + 2c
-2a + ab = -1bc + 2c

Reorder the terms:
-2a + ab + bc + -2c = -1bc + bc + 2c + -2c

Combine like terms: -1bc + bc = 0
-2a + ab + bc + -2c = 0 + 2c + -2c
-2a + ab + bc + -2c = 2c + -2c

Combine like terms: 2c + -2c = 0
-2a + ab + bc + -2c = 0

The solution to this equation could not be determined.