Solve for x (x+yi)+(2(x+yi)+3i)=9

$(x + y i) + (2 (x + y i) + 3 i) = 9$

Simplify $x + y i + 2 (x + y i) + 3 i$ .

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Apply the distributive property.

$x + y i + 2 x + 2 y i + 3 i = 9$

Simplify by adding terms.

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Add $x$ and $2 x$ .

$y i + 3 x + 2 y i + 3 i = 9$

Add $y i$ and $2 y i$ .

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

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

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Subtract $3 y i$ from both sides of the equation.

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

Subtract $3 i$ from both sides of the equation.

$3 x = 9 - 3 y i - 3 i$

Divide each term by $3$ and simplify.

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

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

Cancel the common factor of $3$ .

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Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify each term.

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Divide $9$ by $3$ .

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

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

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Factor $3$ out of $- 3 y i$ .

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

Cancel the common factors.

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Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- y i$ by $1$ .

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

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

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Factor $3$ out of $- 3 i$ .

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

Cancel the common factors.

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Factor $3$ out of $3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $- i$ by $1$ .

$x = 3 - y i - i$

Solve for x (x+yi)+(2(x+yi)+3i)=9

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