Solve for x 9+12i=3x+4yi

$9 + 12 i = 3 x + 4 y i$

Rewrite the equation as $3 x + 4 y i = 9 + 12 i$ .

$3 x + 4 y i = 9 + 12 i$

Subtract $4 y i$ from both sides of the equation.

$3 x = 9 + 12 i - 4 y i$

Divide each term in $3 x = 9 + 12 i - 4 y i$ by $3$ and simplify.

Divide each term in $3 x = 9 + 12 i - 4 y i$ by $3$ .

$\frac{3 x}{3} = \frac{9}{3} + \frac{12 i}{3} + \frac{- 4 y i}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{9}{3} + \frac{12 i}{3} + \frac{- 4 y i}{3}$

Divide $x$ by $1$ .

$x = \frac{9}{3} + \frac{12 i}{3} + \frac{- 4 y i}{3}$

Simplify the right side.

Simplify each term.

Divide $9$ by $3$ .

$x = 3 + \frac{12 i}{3} + \frac{- 4 y i}{3}$

Cancel the common factor of $12$ and $3$ .

Factor $3$ out of $12 i$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $4 i$ by $1$ .

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

Move the negative in front of the fraction.

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