bx=ab+bc

Solution for bx=ab+bc equation:

Simplifying
bx = ab + bc

Solving
bx = ab + bc

Solving for variable 'b'.

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

Add '-1ab' to each side of the equation.
-1ab + bx = ab + -1ab + bc

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

Add '-1bc' to each side of the equation.
-1ab + -1bc + bx = bc + -1bc

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

Factor out the Greatest Common Factor (GCF), 'b'.
b(-1a + -1c + x) = 0

Subproblem 1
Set the factor 'b' equal to zero and attempt to solve:

Simplifying
b = 0

Solving
b = 0

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

Simplifying
b = 0
Subproblem 2
Set the factor '(-1a + -1c + x)' equal to zero and attempt to solve:

Simplifying
-1a + -1c + x = 0

Solving
-1a + -1c + x = 0

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

Add 'a' to each side of the equation.
-1a + -1c + a + x = 0 + a

Reorder the terms:
-1a + a + -1c + x = 0 + a

Combine like terms: -1a + a = 0
0 + -1c + x = 0 + a
-1c + x = 0 + a
Remove the zero:
-1c + x = a

Add 'c' to each side of the equation.
-1c + c + x = a + c

Combine like terms: -1c + c = 0
0 + x = a + c
x = a + c

Add '-1x' to each side of the equation.
x + -1x = a + c + -1x

Combine like terms: x + -1x = 0
0 = a + c + -1x

Simplifying
0 = a + c + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
b = {0}