Simplify and Solve: Combining Fractions and Decimals in 6 4/5x + 7 1/2x + 4 1/3x * 7.3x = ?

To solve this problem, we need to follow a systematic approach:

• Step 1: Convert all mixed numbers into improper fractions.
• Step 2: Carry out the multiplication between the terms $4\frac{1}{3}x \cdot 7.3x$.
• Step 3: Combine the terms by adding the coefficients of $x$ and $x^2$.

Let's proceed with these steps:
Step 1: Convert mixed numbers to improper fractions.
$6\frac{4}{5}x = \left(\frac{34}{5}\right)x$ $7\frac{1}{2}x = \left(\frac{15}{2}\right)x$ $4\frac{1}{3} = \frac{13}{3}$ Step 2: Compute the multiplication and product.
$\left(\frac{13}{3}\right)x \cdot 7.3x = \left(\frac{13}{3} \cdot 7.3\right)x^2 = \left(\frac{94.9}{3}\right)x^2$ Approximate $\frac{94.9}{3} = 31.633...$ or convert to a fraction $31\frac{19}{30}$.
Step 3: Combine all like terms by their variables.
$\left(\frac{34}{5}\right)x + \left(\frac{15}{2}\right)x + 31\frac{19}{30}x^2$ Converting to decimal form: $6.8x + 7.5x = 14.3x$ Thus, the final expression combines neatly as:
$14.3x + 31\frac{19}{30}x^2$

After reviewing the steps and calculations, the solution to the expression is $14.3x + 31\frac{19}{30}x^2$.