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4\left(3p+1-2p-1\right)=5p
Multiply both sides of the equation by 12, the least common multiple of 3,12.
4\left(p+1-1\right)=5p
Combine 3p and -2p to get p.
4p=5p
Subtract 1 from 1 to get 0.
4p-5p=0
Subtract 5p from both sides.
-p=0
Combine 4p and -5p to get -p.
p=0
Product of two numbers is equal to 0 if at least one of them is 0. Since -1 is not equal to 0, p must be equal to 0.