2=(p-2)(p-3)

p = 1 or p = 4

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.