(.5p-8)(.25p-1)=0

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Solution for (.5p-8)(.25p-1)=0 equation:


Simplifying
(0.5p + -8)(0.25p + -1) = 0

Reorder the terms:
(-8 + 0.5p)(0.25p + -1) = 0

Reorder the terms:
(-8 + 0.5p)(-1 + 0.25p) = 0

Multiply (-8 + 0.5p) * (-1 + 0.25p)
(-8(-1 + 0.25p) + 0.5p * (-1 + 0.25p)) = 0
((-1 * -8 + 0.25p * -8) + 0.5p * (-1 + 0.25p)) = 0
((8 + -2p) + 0.5p * (-1 + 0.25p)) = 0
(8 + -2p + (-1 * 0.5p + 0.25p * 0.5p)) = 0
(8 + -2p + (-0.5p + 0.125p2)) = 0

Combine like terms: -2p + -0.5p = -2.5p
(8 + -2.5p + 0.125p2) = 0

Solving
8 + -2.5p + 0.125p2 = 0

Solving for variable 'p'.

Begin completing the square.  Divide all terms by
0.125 the coefficient of the squared term: 

Divide each side by '0.125'.
64 + -20p + p2 = 0

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -20p + -64 + p2 = 0 + -64

Reorder the terms:
64 + -64 + -20p + p2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -20p + p2 = 0 + -64
-20p + p2 = 0 + -64

Combine like terms: 0 + -64 = -64
-20p + p2 = -64

The p term is -20p.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20p + 100 + p2 = -64 + 100

Reorder the terms:
100 + -20p + p2 = -64 + 100

Combine like terms: -64 + 100 = 36
100 + -20p + p2 = 36

Factor a perfect square on the left side:
(p + -10)(p + -10) = 36

Calculate the square root of the right side: 6

Break this problem into two subproblems by setting 
(p + -10) equal to 6 and -6.

Subproblem 1

p + -10 = 6 Simplifying p + -10 = 6 Reorder the terms: -10 + p = 6 Solving -10 + p = 6 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = 6 + 10 Combine like terms: -10 + 10 = 0 0 + p = 6 + 10 p = 6 + 10 Combine like terms: 6 + 10 = 16 p = 16 Simplifying p = 16

Subproblem 2

p + -10 = -6 Simplifying p + -10 = -6 Reorder the terms: -10 + p = -6 Solving -10 + p = -6 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + p = -6 + 10 Combine like terms: -10 + 10 = 0 0 + p = -6 + 10 p = -6 + 10 Combine like terms: -6 + 10 = 4 p = 4 Simplifying p = 4

Solution

The solution to the problem is based on the solutions from the subproblems. p = {16, 4}

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