Answer
$$(-4+3i)x\cdot(-12+6i)=18i^2x-60ix+48x$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-4+3i)x\cdot(-12+6i)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(-4x+3ix)\cdot(-12+6i) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}48x-24ix-36ix+18i^2x \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18i^2x-60ix+48x\end{aligned} $$ | |
| ① | $$ \left( \color{blue}{-4+3i}\right) \cdot x = -4x+3ix $$ |
| ② | Multiply each term of $ \left( \color{blue}{-4x+3ix}\right) $ by each term in $ \left( -12+6i\right) $. $$ \left( \color{blue}{-4x+3ix}\right) \cdot \left( -12+6i\right) = 48x-24ix-36ix+18i^2x $$ |
| ③ | Combine like terms: $$ 48x \color{blue}{-24ix} \color{blue}{-36ix} +18i^2x = 18i^2x \color{blue}{-60ix} +48x $$ |
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