$$ 3i^5 = 3 \cdot i^{4 \cdot 1 + 1} = 3 \cdot \left( i^4 \right)^{ 1 } \cdot i^1 = 3 \cdot 1^{ 1 } \cdot i = 3 \cdot i $$

Divide $ \, 5+5i \, $ by $ \, -2i \, $ to get $\,\, \dfrac{-5+5i}{2} $.
( view steps )

Multiply $6$ by $ \dfrac{-5+5i}{2} $ to get $ \dfrac{30i-30}{2} $.

Step 1: Write $ 6 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} 6 \cdot \frac{-5+5i}{2} & \xlongequal{\text{Step 1}} \frac{6}{\color{red}{1}} \cdot \frac{-5+5i}{2} \xlongequal{\text{Step 2}} \frac{ 6 \cdot \left( -5+5i \right) }{ 1 \cdot 2 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ -30+30i }{ 2 } = \frac{30i-30}{2} \end{aligned} $$

Multiply $ \dfrac{30i-30}{2} $ by $ 3i $ to get $ \dfrac{ 90i^2-90i }{ 2 } $.

Step 1: Write $ 3i $ as a fraction by putting $ \color{red}{ 1 } $ in the denominator.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{30i-30}{2} \cdot 3i & \xlongequal{\text{Step 1}} \frac{30i-30}{2} \cdot \frac{3i}{\color{red}{1}} \xlongequal{\text{Step 2}} \frac{ \left( 30i-30 \right) \cdot 3i }{ 2 \cdot 1 } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 90i^2-90i }{ 2 } \end{aligned} $$

$$ 90i^2 = 90 \cdot (-1) = -90 $$