Multiply $ \color{blue}{2} $ by $ \left( x-4\right) $ $$ \color{blue}{2} \cdot \left( x-4\right) = 2x-8 $$

Multiply each term of $ \left( \color{blue}{2x-8}\right) $ by each term in $ \left( x+3\right) $.

$$ \left( \color{blue}{2x-8}\right) \cdot \left( x+3\right) = 2x^2+6x-8x-24 $$

Combine like terms:

$$ 2x^2+ \color{blue}{6x} \color{blue}{-8x} -24 = 2x^2 \color{blue}{-2x} -24 $$

Multiply $5x^2-30x+40$ by $ \dfrac{x+1}{2x^2-2x-24} $ to get $ \dfrac{5x^2-5x-10}{2x+6} $.

Step 1: Write $ 5x^2-30x+40 $ as a fraction by putting $ \color{red}{1} $ in the denominator.

Step 2: Factor numerators and denominators.

Step 3: Cancel common factors.

Step 4: Multiply numerators and denominators.

Step 5: Simplify numerator and denominator.

$$ \begin{aligned} 5x^2-30x+40 \cdot \frac{x+1}{2x^2-2x-24} & \xlongequal{\text{Step 1}} \frac{5x^2-30x+40}{\color{red}{1}} \cdot \frac{x+1}{2x^2-2x-24} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ \left( 5x-10 \right) \cdot \color{blue}{ \left( x-4 \right) } }{ 1 } \cdot \frac{ x+1 }{ \left( 2x+6 \right) \cdot \color{blue}{ \left( x-4 \right) } } = \\[1ex] & \xlongequal{\text{Step 3}} \frac{ 5x-10 }{ 1 } \cdot \frac{ x+1 }{ 2x+6 } \xlongequal{\text{Step 4}} \frac{ \left( 5x-10 \right) \cdot \left( x+1 \right) }{ 1 \cdot \left( 2x+6 \right) } = \\[1ex] & \xlongequal{\text{Step 5}} \frac{ 5x^2+5x-10x-10 }{ 2x+6 } = \frac{5x^2-5x-10}{2x+6} \end{aligned} $$