(p-2)(p-8)=7

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Solution for (p-2)(p-8)=7 equation: 


Simplifying
(p + -2)(p + -8) = 7

Reorder the terms:
(-2 + p)(p + -8) = 7

Reorder the terms:
(-2 + p)(-8 + p) = 7

Multiply (-2 + p) * (-8 + p)
(-2(-8 + p) + p(-8 + p)) = 7
((-8 * -2 + p * -2) + p(-8 + p)) = 7
((16 + -2p) + p(-8 + p)) = 7
(16 + -2p + (-8 * p + p * p)) = 7
(16 + -2p + (-8p + p2)) = 7

Combine like terms: -2p + -8p = -10p
(16 + -10p + p2) = 7

Solving
16 + -10p + p2 = 7

Solving for variable 'p'.

Reorder the terms:
16 + -7 + -10p + p2 = 7 + -7

Combine like terms: 16 + -7 = 9
9 + -10p + p2 = 7 + -7

Combine like terms: 7 + -7 = 0
9 + -10p + p2 = 0

Factor a trinomial.
(1 + -1p)(9 + -1p) = 0


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

Simplifying
1 + -1p = 0

Solving
1 + -1p = 0

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

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

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

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

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

Simplifying
p = 1

Subproblem 2
Set the factor '(9 + -1p)' equal to zero and attempt to solve:

Simplifying
9 + -1p = 0

Solving
9 + -1p = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1p = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1p = 0 + -9
-1p = 0 + -9

Combine like terms: 0 + -9 = -9
-1p = -9

Divide each side by '-1'.
p = 9

Simplifying
p = 9
Solution
p = {1, 9}

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