a+ab+abc=abcd

Solution for a+ab+abc=abcd equation:

Simplifying
a + ab + abc = abcd

Solving
a + ab + abc = abcd

Solving for variable 'a'.

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

Add '-1abcd' to each side of the equation.
a + ab + abc + -1abcd = abcd + -1abcd

Combine like terms: abcd + -1abcd = 0
a + ab + abc + -1abcd = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(1 + b + bc + -1bcd) = 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 '(1 + b + bc + -1bcd)' equal to zero and attempt to solve:

Simplifying
1 + b + bc + -1bcd = 0

Solving
1 + b + bc + -1bcd = 0

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

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

Reorder the terms:
1 + -1 + b + bc + -1bcd = 0 + -1

Combine like terms: 1 + -1 = 0
0 + b + bc + -1bcd = 0 + -1
b + bc + -1bcd = 0 + -1

Combine like terms: 0 + -1 = -1
b + bc + -1bcd = -1

Add '-1b' to each side of the equation.
b + bc + -1b + -1bcd = -1 + -1b

Reorder the terms:
b + -1b + bc + -1bcd = -1 + -1b

Combine like terms: b + -1b = 0
0 + bc + -1bcd = -1 + -1b
bc + -1bcd = -1 + -1b

Add '-1bc' to each side of the equation.
bc + -1bc + -1bcd = -1 + -1b + -1bc

Combine like terms: bc + -1bc = 0
0 + -1bcd = -1 + -1b + -1bc
-1bcd = -1 + -1b + -1bc

Add 'bcd' to each side of the equation.
-1bcd + bcd = -1 + -1b + -1bc + bcd

Combine like terms: -1bcd + bcd = 0
0 = -1 + -1b + -1bc + bcd

Simplifying
0 = -1 + -1b + -1bc + bcd

The solution to this equation could not be determined.

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