Solve for x -10x+12i=20+3yi

$- 10 x + 12 i = 20 + 3 y i$

Subtract $12 i$ from both sides of the equation.

$- 10 x = 20 + 3 y i - 12 i$

Divide each term in $- 10 x = 20 + 3 y i - 12 i$ by $- 10$ and simplify.

Divide each term in $- 10 x = 20 + 3 y i - 12 i$ by $- 10$ .

$\frac{- 10 x}{- 10} = \frac{20}{- 10} + \frac{3 y i}{- 10} + \frac{- 12 i}{- 10}$

Simplify the left side.

Cancel the common factor of $- 10$ .

Cancel the common factor.

$\frac{- 10 x}{- 10} = \frac{20}{- 10} + \frac{3 y i}{- 10} + \frac{- 12 i}{- 10}$

Divide $x$ by $1$ .

$x = \frac{20}{- 10} + \frac{3 y i}{- 10} + \frac{- 12 i}{- 10}$

Simplify the right side.

Simplify each term.

Divide $20$ by $- 10$ .

$x = - 2 + \frac{3 y i}{- 10} + \frac{- 12 i}{- 10}$

Move the negative in front of the fraction.

$x = - 2 - \frac{3 y i}{10} + \frac{- 12 i}{- 10}$

Cancel the common factor of $- 12$ and $- 10$ .

Factor $- 2$ out of $- 12 i$ .

$x = - 2 - \frac{3 y i}{10} + \frac{- 2 (6 i)}{- 10}$

Cancel the common factors.

Factor $- 2$ out of $- 10$ .

$x = - 2 - \frac{3 y i}{10} + \frac{- 2 (6 i)}{- 2 (5)}$

Cancel the common factor.

$x = - 2 - \frac{3 y i}{10} + \frac{- 2 (6 i)}{- 2 \cdot 5}$

Rewrite the expression.

$x = - 2 - \frac{3 y i}{10} + \frac{6 i}{5}$