jmc

We need to simplify the given expression. Let's start by simplifying the inside of the parenthesis on the left part of the expression. $$\begin{array}{rl}((5p+1)& -2p\cdot 4)(3)+(4-1÷3)(6p-9)\\ & =(5p+1-8p)(3)+(4-1÷3)(6p-9)\\ & =(-3p+1)(3)+(4-1÷3)(6p-9)\end{array}$$ Next we can distribute the 3 to get $$3\cdot (-3p)+3\cdot 1+(4-1÷3)(6p-9),$$ which equals $-9p+3+(4-1÷3)(6p-9)$ . The left part looks simplified so now we can focus on the right part. Let's subtract what's in the left parentheses then distribute. $$\begin{array}{rl}-9p+3+(4-1÷3)(6p-9)& =-9p+3+(\frac{4\cdot 3}{3}-\frac{1}{3})(6p-9)\\ & =-9p+3+\frac{11}{3}(6p-9)\\ & =-9p+3+\frac{11}{3}\cdot 6p-\frac{11}{3}\cdot 9\\ & =-9p+3+\frac{11\cdot 6p}{3}-\frac{11\cdot 9}{3}\\ & =-9p+3+\frac{66p}{3}-\frac{99}{3}\\ & =-9p+3+\frac{3\cdot 22p}{3}-\frac{3\cdot 33}{3}\\ & =-9p+3+22p-33\\ & =22p-9p+3-33\\ & =\boxed{13p-30}\end{array}$$