(p-6)(p-7)=0

Solution for (p-6)(p-7)=0 equation:

Simplifying
(p + -6)(p + -7) = 0

Reorder the terms:
(-6 + p)(p + -7) = 0

Reorder the terms:
(-6 + p)(-7 + p) = 0

Multiply (-6 + p) * (-7 + p)
(-6(-7 + p) + p(-7 + p)) = 0
((-7 * -6 + p * -6) + p(-7 + p)) = 0
((42 + -6p) + p(-7 + p)) = 0
(42 + -6p + (-7 * p + p * p)) = 0
(42 + -6p + (-7p + p2)) = 0

Combine like terms: -6p + -7p = -13p
(42 + -13p + p2) = 0

Solving
42 + -13p + p2 = 0

Solving for variable 'p'.

Factor a trinomial.
(6 + -1p)(7 + -1p) = 0

Subproblem 1
Set the factor '(6 + -1p)' equal to zero and attempt to solve:

Simplifying
6 + -1p = 0

Solving
6 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1p = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1p = 0 + -6
-1p = 0 + -6

Combine like terms: 0 + -6 = -6
-1p = -6

Divide each side by '-1'.
p = 6

Simplifying
p = 6
Subproblem 2
Set the factor '(7 + -1p)' equal to zero and attempt to solve:

Simplifying
7 + -1p = 0

Solving
7 + -1p = 0

Move all terms containing p to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1p = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1p = 0 + -7
-1p = 0 + -7

Combine like terms: 0 + -7 = -7
-1p = -7

Divide each side by '-1'.
p = 7

Simplifying
p = 7
Solution
p = {6, 7}