The problem requires expanding the expression $(5x+1)(x-2)$.

1. Problem Description

The problem requires expanding the expression $(5x+1)(x-2)$.

2. Solution Steps

We will use the distributive property (also known as the FOIL method) to expand the expression:

$(a+b)(c+d) = ac + ad + bc + bd$

Applying this to our expression $(5x+1)(x-2)$:

$(5x+1)(x-2) = (5x)(x) + (5x)(-2) + (1)(x) + (1)(-2)$

$= 5x^2 -10x + x - 2$

Now, combine like terms:

$= 5x^2 + (-10x + x) - 2$

$= 5x^2 - 9x - 2$

3. Final Answer

$5x^2 - 9x - 2$