a(b+c)=axb+axc

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Solution for a(b+c)=axb+axc equation: 


Simplifying
a(b + c) = axb + axc
(b * a + c * a) = axb + axc
(ab + ac) = axb + axc

Solving
ab + ac = abx + acx

Solving for variable 'a'.

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

Add '-1abx' to each side of the equation.
ab + -1abx + ac = abx + -1abx + acx

Combine like terms: abx + -1abx = 0
ab + -1abx + ac = 0 + acx
ab + -1abx + ac = acx

Add '-1acx' to each side of the equation.
ab + -1abx + ac + -1acx = acx + -1acx

Combine like terms: acx + -1acx = 0
ab + -1abx + ac + -1acx = 0

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


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(b + -1bx + c + -1cx)' equal to zero and attempt to solve:

Simplifying
b + -1bx + c + -1cx = 0

Solving
b + -1bx + c + -1cx = 0

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

Add '-1b' to each side of the equation.
b + -1bx + c + -1b + -1cx = 0 + -1b

Reorder the terms:
b + -1b + -1bx + c + -1cx = 0 + -1b

Combine like terms: b + -1b = 0
0 + -1bx + c + -1cx = 0 + -1b
-1bx + c + -1cx = 0 + -1b
Remove the zero:
-1bx + c + -1cx = -1b

Add 'bx' to each side of the equation.
-1bx + c + bx + -1cx = -1b + bx

Reorder the terms:
-1bx + bx + c + -1cx = -1b + bx

Combine like terms: -1bx + bx = 0
0 + c + -1cx = -1b + bx
c + -1cx = -1b + bx

Add '-1c' to each side of the equation.
c + -1c + -1cx = -1b + bx + -1c

Combine like terms: c + -1c = 0
0 + -1cx = -1b + bx + -1c
-1cx = -1b + bx + -1c

Add 'cx' to each side of the equation.
-1cx + cx = -1b + bx + -1c + cx

Combine like terms: -1cx + cx = 0
0 = -1b + bx + -1c + cx

Simplifying
0 = -1b + bx + -1c + cx

The solution to this equation could not be determined.

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

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