(6+3i)+(14-7i)-(a-bi)=0

Solution for (6+3i)+(14-7i)-(a-bi)=0 equation:

Simplifying
(6 + 3i) + (14 + -7i) + -1(a + -1bi) = 0

Remove parenthesis around (6 + 3i)
6 + 3i + (14 + -7i) + -1(a + -1bi) = 0

Remove parenthesis around (14 + -7i)
6 + 3i + 14 + -7i + -1(a + -1bi) = 0
6 + 3i + 14 + -7i + (a * -1 + -1bi * -1) = 0
6 + 3i + 14 + -7i + (-1a + 1bi) = 0

Reorder the terms:
6 + 14 + -1a + 1bi + 3i + -7i = 0

Combine like terms: 6 + 14 = 20
20 + -1a + 1bi + 3i + -7i = 0

Combine like terms: 3i + -7i = -4i
20 + -1a + 1bi + -4i = 0

Solving
20 + -1a + 1bi + -4i = 0

Solving for variable 'a'.

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

Add '-20' to each side of the equation.
20 + -1a + 1bi + -20 + -4i = 0 + -20

Reorder the terms:
20 + -20 + -1a + 1bi + -4i = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1a + 1bi + -4i = 0 + -20
-1a + 1bi + -4i = 0 + -20

Combine like terms: 0 + -20 = -20
-1a + 1bi + -4i = -20

Add '-1bi' to each side of the equation.
-1a + 1bi + -1bi + -4i = -20 + -1bi

Combine like terms: 1bi + -1bi = 0
-1a + 0 + -4i = -20 + -1bi
-1a + -4i = -20 + -1bi

Add '4i' to each side of the equation.
-1a + -4i + 4i = -20 + -1bi + 4i

Combine like terms: -4i + 4i = 0
-1a + 0 = -20 + -1bi + 4i
-1a = -20 + -1bi + 4i

Divide each side by '-1'.
a = 20 + bi + -4i

Simplifying
a = 20 + bi + -4i