Could you some help understanding the steps to solve this equation

$148.72
1) Gathering the data
Original Price: $260
Discount rate: 45%
Sales Tax rate: 4%
2) Since that man received a 45% off discount then, let's find the Discounted Price, using an equation for that:
[tex]\begin{gathered} 260\times(1-0.45)= \\ 260\times(0.55)= \\ 143 \end{gathered}[/tex]So after that 45% off the price has dropped to $143
2.2) But the State where he lives charges 4% so we can write another equation, similar to previous item 2, this time the factor is (1 +0.04), like this:
[tex]143\times(1+0.04)=148.72[/tex]Hence, the total bill for that washer is $148.72