ab+3a=a(b+i)

Solution for ab+3a=a(b+i) equation:

Simplifying
ab + 3a = a(b + i)

Reorder the terms:
3a + ab = a(b + i)
3a + ab = (b * a + i * a)
3a + ab = (ab + ai)

Add '-1ab' to each side of the equation.
3a + ab + -1ab = ab + -1ab + ai

Combine like terms: ab + -1ab = 0
3a + 0 = ab + -1ab + ai
3a = ab + -1ab + ai

Combine like terms: ab + -1ab = 0
3a = 0 + ai
3a = ai

Solving
3a = ai

Solving for variable 'a'.

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

Add '-1ai' to each side of the equation.
3a + -1ai = ai + -1ai

Combine like terms: ai + -1ai = 0
3a + -1ai = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(3 + -1i) = 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 '(3 + -1i)' equal to zero and attempt to solve:

Simplifying
3 + -1i = 0

Solving
3 + -1i = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1i = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1i = 0 + -3
-1i = 0 + -3

Combine like terms: 0 + -3 = -3
-1i = -3

Add 'i' to each side of the equation.
-1i + i = -3 + i

Combine like terms: -1i + i = 0
0 = -3 + i

Simplifying
0 = -3 + i

The solution to this equation could not be determined.

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