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

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

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

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

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

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

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

Combine like terms: -3i + -7i = -10i
20 + -1a + -1b + -10i = 0

Solving
20 + -1a + -1b + -10i = 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 + -1b + -20 + -10i = 0 + -20

Reorder the terms:
20 + -20 + -1a + -1b + -10i = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1a + -1b + -10i = 0 + -20
-1a + -1b + -10i = 0 + -20

Combine like terms: 0 + -20 = -20
-1a + -1b + -10i = -20

Add 'b' to each side of the equation.
-1a + -1b + b + -10i = -20 + b

Combine like terms: -1b + b = 0
-1a + 0 + -10i = -20 + b
-1a + -10i = -20 + b

Add '10i' to each side of the equation.
-1a + -10i + 10i = -20 + b + 10i

Combine like terms: -10i + 10i = 0
-1a + 0 = -20 + b + 10i
-1a = -20 + b + 10i

Divide each side by '-1'.
a = 20 + -1b + -10i

Simplifying
a = 20 + -1b + -10i