(p-8)(p-2)=-5

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Solution for (p-8)(p-2)=-5 equation: 


Simplifying
(p + -8)(p + -2) = -5

Reorder the terms:
(-8 + p)(p + -2) = -5

Reorder the terms:
(-8 + p)(-2 + p) = -5

Multiply (-8 + p) * (-2 + p)
(-8(-2 + p) + p(-2 + p)) = -5
((-2 * -8 + p * -8) + p(-2 + p)) = -5
((16 + -8p) + p(-2 + p)) = -5
(16 + -8p + (-2 * p + p * p)) = -5
(16 + -8p + (-2p + p2)) = -5

Combine like terms: -8p + -2p = -10p
(16 + -10p + p2) = -5

Solving
16 + -10p + p2 = -5

Solving for variable 'p'.

Reorder the terms:
16 + 5 + -10p + p2 = -5 + 5

Combine like terms: 16 + 5 = 21
21 + -10p + p2 = -5 + 5

Combine like terms: -5 + 5 = 0
21 + -10p + p2 = 0

Factor a trinomial.
(3 + -1p)(7 + -1p) = 0


Subproblem 1
Set the factor '(3 + -1p)' equal to zero and attempt to solve:

Simplifying
3 + -1p = 0

Solving
3 + -1p = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3

Combine like terms: 0 + -3 = -3
-1p = -3

Divide each side by '-1'.
p = 3

Simplifying
p = 3

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 = {3, 7}

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