(2-ai)(3-bi)=8+4i

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Solution for (2-ai)(3-bi)=8+4i equation: 


Simplifying
(2 + -1ai)(3 + -1bi) = 8 + 4i

Multiply (2 + -1ai) * (3 + -1bi)
(2(3 + -1bi) + -1ai * (3 + -1bi)) = 8 + 4i
((3 * 2 + -1bi * 2) + -1ai * (3 + -1bi)) = 8 + 4i
((6 + -2bi) + -1ai * (3 + -1bi)) = 8 + 4i
(6 + -2bi + (3 * -1ai + -1bi * -1ai)) = 8 + 4i

Reorder the terms:
(6 + -2bi + (1abi2 + -3ai)) = 8 + 4i
(6 + -2bi + (1abi2 + -3ai)) = 8 + 4i

Reorder the terms:
(6 + 1abi2 + -3ai + -2bi) = 8 + 4i
(6 + 1abi2 + -3ai + -2bi) = 8 + 4i

Solving
6 + 1abi2 + -3ai + -2bi = 8 + 4i

Solving for variable 'a'.

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

Add '-6' to each side of the equation.
6 + 1abi2 + -3ai + -6 + -2bi = 8 + -6 + 4i

Reorder the terms:
6 + -6 + 1abi2 + -3ai + -2bi = 8 + -6 + 4i

Combine like terms: 6 + -6 = 0
0 + 1abi2 + -3ai + -2bi = 8 + -6 + 4i
1abi2 + -3ai + -2bi = 8 + -6 + 4i

Combine like terms: 8 + -6 = 2
1abi2 + -3ai + -2bi = 2 + 4i

Add '2bi' to each side of the equation.
1abi2 + -3ai + -2bi + 2bi = 2 + 2bi + 4i

Combine like terms: -2bi + 2bi = 0
1abi2 + -3ai + 0 = 2 + 2bi + 4i
1abi2 + -3ai = 2 + 2bi + 4i

Reorder the terms:
-2 + 1abi2 + -3ai + -2bi + -4i = 2 + 2bi + 4i + -2 + -2bi + -4i

Reorder the terms:
-2 + 1abi2 + -3ai + -2bi + -4i = 2 + -2 + 2bi + -2bi + 4i + -4i

Combine like terms: 2 + -2 = 0
-2 + 1abi2 + -3ai + -2bi + -4i = 0 + 2bi + -2bi + 4i + -4i
-2 + 1abi2 + -3ai + -2bi + -4i = 2bi + -2bi + 4i + -4i

Combine like terms: 2bi + -2bi = 0
-2 + 1abi2 + -3ai + -2bi + -4i = 0 + 4i + -4i
-2 + 1abi2 + -3ai + -2bi + -4i = 4i + -4i

Combine like terms: 4i + -4i = 0
-2 + 1abi2 + -3ai + -2bi + -4i = 0

The solution to this equation could not be determined.

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