We are asked to multiply the two binomials $(9x + 6)$ and $(5x + 3)$ and simplify the result.

1. Problem Description

We are asked to multiply the two binomials $(9x + 6)$ and $(5x + 3)$ and simplify the result.

2. Solution Steps

To multiply the two binomials $(9x+6)(5x+3)$, we use the distributive property (also known as the FOIL method).

First: $(9x)(5x) = 45x^2$

Outer: $(9x)(3) = 27x$

Inner: $(6)(5x) = 30x$

Last: $(6)(3) = 18$

So,

$(9x+6)(5x+3) = (9x)(5x) + (9x)(3) + (6)(5x) + (6)(3) = 45x^2 + 27x + 30x + 18$.

Now, we combine like terms: $27x + 30x = 57x$.

Therefore, the simplified expression is $45x^2 + 57x + 18$.

3. Final Answer

$45x^2 + 57x + 18$