Solve for y 2x-yi=14+12i

$2 x - y i = 14 + 12 i$

Subtract $2 x$ from both sides of the equation.

$- y i = 14 + 12 i - 2 x$

Divide each term in $- y i = 14 + 12 i - 2 x$ by $- i$ and simplify.

Divide each term in $- y i = 14 + 12 i - 2 x$ by $- i$ .

$\frac{- y i}{- i} = \frac{14}{- i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y i}{i} = \frac{14}{- i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{y i}{i} = \frac{14}{- i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Divide $y$ by $1$ .

$y = \frac{14}{- i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Simplify the right side.

Simplify each term.

Multiply the numerator and denominator of $\frac{14}{- i}$ by the conjugate of $- i$ to make the denominator real.

$y = \frac{14}{- i} \cdot \frac{i}{i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Multiply.

Combine.

$y = \frac{14 i}{- i i} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Simplify the denominator.

Add parentheses.

$y = \frac{14 i}{- (i i)} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Raise $i$ to the power of $1$ .

$y = \frac{14 i}{- (i^{1} i)} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Raise $i$ to the power of $1$ .

$y = \frac{14 i}{- (i^{1} i^{1})} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = \frac{14 i}{- i^{1 + 1}} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Add $1$ and $1$ .

$y = \frac{14 i}{- i^{2}} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Rewrite $i^{2}$ as $- 1$ .

$y = \frac{14 i}{- - 1} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Multiply $- 1$ by $- 1$ .

$y = \frac{14 i}{1} + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Divide $14 i$ by $1$ .

$y = 14 i + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$y = 14 i + \frac{12 i}{- i} + \frac{- 2 x}{- i}$

Rewrite the expression.

$y = 14 i + \frac{12}{- 1} + \frac{- 2 x}{- i}$

Move the negative one from the denominator of $\frac{12}{- 1}$ .

$y = 14 i - 1 \cdot 12 + \frac{- 2 x}{- i}$

Multiply $- 1$ by $12$ .

$y = 14 i - 12 + \frac{- 2 x}{- i}$

Multiply the numerator and denominator of $\frac{- 2 x}{- i}$ by the conjugate of $- i$ to make the denominator real.

$y = 14 i - 12 + \frac{- 2 x}{- i} \cdot \frac{i}{i}$

Multiply.

Combine.

$y = 14 i - 12 + \frac{- 2 x i}{- i i}$

Simplify the denominator.

Add parentheses.

$y = 14 i - 12 + \frac{- 2 x i}{- (i i)}$

Raise $i$ to the power of $1$ .

$y = 14 i - 12 + \frac{- 2 x i}{- (i^{1} i)}$

Raise $i$ to the power of $1$ .

$y = 14 i - 12 + \frac{- 2 x i}{- (i^{1} i^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$y = 14 i - 12 + \frac{- 2 x i}{- i^{1 + 1}}$

Add $1$ and $1$ .

$y = 14 i - 12 + \frac{- 2 x i}{- i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$y = 14 i - 12 + \frac{- 2 x i}{- - 1}$

Multiply $- 1$ by $- 1$ .

$y = 14 i - 12 + \frac{- 2 x i}{1}$

Divide $- 2 x i$ by $1$ .

$y = 14 i - 12 - 2 x i$

Reorder $14 i$ and $- 12$ .

$y = - 12 + 14 i - 2 x i$

Solve for y 2x-yi=14+12i

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