Solve for x 2x+8i=6-(2y)i

$2 x + 8 i = 6 - (2 y) i$

Step 1

Subtract $8 i$ from both sides of the equation.

$2 x = 6 - 2 y i - 8 i$

Step 2

Divide each term in $2 x = 6 - 2 y i - 8 i$ by $2$ and simplify.

Divide each term in $2 x = 6 - 2 y i - 8 i$ by $2$ .

$\frac{2 x}{2} = \frac{6}{2} + \frac{- 2 y i}{2} + \frac{- 8 i}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{6}{2} + \frac{- 2 y i}{2} + \frac{- 8 i}{2}$

Divide $x$ by $1$ .

$x = \frac{6}{2} + \frac{- 2 y i}{2} + \frac{- 8 i}{2}$

Simplify the right side.

Simplify each term.

Divide $6$ by $2$ .

$x = 3 + \frac{- 2 y i}{2} + \frac{- 8 i}{2}$

Cancel the common factor of $- 2$ and $2$ .

Factor $2$ out of $- 2 y i$ .

$x = 3 + \frac{2 (- y i)}{2} + \frac{- 8 i}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 3 + \frac{2 (- y i)}{2 (1)} + \frac{- 8 i}{2}$

Cancel the common factor.

$x = 3 + \frac{2 (- y i)}{2 \cdot 1} + \frac{- 8 i}{2}$

Rewrite the expression.

$x = 3 + \frac{- y i}{1} + \frac{- 8 i}{2}$

Divide $- y i$ by $1$ .

$x = 3 - y i + \frac{- 8 i}{2}$

Cancel the common factor of $- 8$ and $2$ .

Factor $2$ out of $- 8 i$ .

$x = 3 - y i + \frac{2 (- 4 i)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$x = 3 - y i + \frac{2 (- 4 i)}{2 (1)}$

Cancel the common factor.

$x = 3 - y i + \frac{2 (- 4 i)}{2 \cdot 1}$

Rewrite the expression.

$x = 3 - y i + \frac{- 4 i}{1}$

Divide $- 4 i$ by $1$ .

$x = 3 - y i - 4 i$