Find All Complex Solutions (4y-5)+(-x-3)i=7-8i

$(4 y - 5) + (- x - 3) i = 7 - 8 i$

Move all terms not containing a variable to the right side of the equation.

Add $5$ to both sides of the equation.

$(4 y) + (- x - 3) i = 7 - 8 i + 5$

Add $7$ and $5$ .

$(4 y) + (- x - 3) i = 12 - 8 i$

Apply the distributive property.

$4 y - x i - 3 i = 12 - 8 i$

Move all terms not containing $y$ to the right side of the equation.

Add $x i$ to both sides of the equation.

$4 y - 3 i = 12 - 8 i + x i$

Add $3 i$ to both sides of the equation.

$4 y = 12 - 8 i + x i + 3 i$

Add $- 8 i$ and $3 i$ .

$4 y = 12 + x i - 5 i$

Divide each term in $4 y = 12 + x i - 5 i$ by $4$ and simplify.

Divide each term in $4 y = 12 + x i - 5 i$ by $4$ .

$\frac{4 y}{4} = \frac{12}{4} + \frac{x i}{4} + \frac{- 5 i}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{12}{4} + \frac{x i}{4} + \frac{- 5 i}{4}$

Divide $y$ by $1$ .

$y = \frac{12}{4} + \frac{x i}{4} + \frac{- 5 i}{4}$

Simplify the right side.

Simplify each term.

Divide $12$ by $4$ .

$y = 3 + \frac{x i}{4} + \frac{- 5 i}{4}$

Move the negative in front of the fraction.

$y = 3 + \frac{x i}{4} - \frac{5 i}{4}$