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To find the values of p that satisfy the equation 2 = (p - 2)(p - 3), we can start by expanding the right side of the equation.
(p - 2)(p - 3) = p^2 - 3p - 2p + 6
= p^2 - 5p + 6
Now we have the equation 2 = p^2 - 5p + 6.
Rearranging the equation, we get p^2 - 5p + 6 - 2 = 0.
Combining like terms, we have p^2 - 5p + 4 = 0.
Now we need to factor this quadratic equation to find its roots. We are looking for two numbers that multiply to give 4 and add up to give -5. Those numbers are -1 and -4.
Factoring, we have (p - 1)(p - 4) = 0.
To solve for p, we set each factor equal to zero:
p - 1 = 0 ---> p = 1
p - 4 = 0 ---> p = 4
Therefore, the values of p that satisfy the equation are p = 1 or p = 4.