6+(x-4)i=6+(3x-5)i

Solution for 6+(x-4)i=6+(3x-5)i equation:

Simplifying
6 + (x + -4) * i = 6 + (3x + -5) * i

Reorder the terms:
6 + (-4 + x) * i = 6 + (3x + -5) * i

Reorder the terms for easier multiplication:
6 + i(-4 + x) = 6 + (3x + -5) * i
6 + (-4 * i + x * i) = 6 + (3x + -5) * i
6 + (-4i + ix) = 6 + (3x + -5) * i

Reorder the terms:
6 + -4i + ix = 6 + (-5 + 3x) * i

Reorder the terms for easier multiplication:
6 + -4i + ix = 6 + i(-5 + 3x)
6 + -4i + ix = 6 + (-5 * i + 3x * i)
6 + -4i + ix = 6 + (-5i + 3ix)

Add '-6' to each side of the equation.
6 + -4i + -6 + ix = 6 + -5i + -6 + 3ix

Reorder the terms:
6 + -6 + -4i + ix = 6 + -5i + -6 + 3ix

Combine like terms: 6 + -6 = 0
0 + -4i + ix = 6 + -5i + -6 + 3ix
-4i + ix = 6 + -5i + -6 + 3ix

Reorder the terms:
-4i + ix = 6 + -6 + -5i + 3ix

Combine like terms: 6 + -6 = 0
-4i + ix = 0 + -5i + 3ix
-4i + ix = -5i + 3ix

Solving
-4i + ix = -5i + 3ix

Solving for variable 'i'.

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

Add '5i' to each side of the equation.
-4i + 5i + ix = -5i + 5i + 3ix

Combine like terms: -4i + 5i = 1i
1i + ix = -5i + 5i + 3ix

Combine like terms: -5i + 5i = 0
1i + ix = 0 + 3ix
1i + ix = 3ix

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

Combine like terms: ix + -3ix = -2ix
1i + -2ix = 3ix + -3ix

Combine like terms: 3ix + -3ix = 0
1i + -2ix = 0

Factor out the Greatest Common Factor (GCF), 'i'.
i(1 + -2x) = 0

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

Simplifying
i = 0

Solving
i = 0

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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Add '2x' to each side of the equation.
-2x + 2x = -1 + 2x

Combine like terms: -2x + 2x = 0
0 = -1 + 2x

Simplifying
0 = -1 + 2x

The solution to this equation could not be determined.

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