p=(p-4)(160+8p)

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Solution for p=(p-4)(160+8p) equation:


Simplifying
p = (p + -4)(160 + 8p)

Reorder the terms:
p = (-4 + p)(160 + 8p)

Multiply (-4 + p) * (160 + 8p)
p = (-4(160 + 8p) + p(160 + 8p))
p = ((160 * -4 + 8p * -4) + p(160 + 8p))
p = ((-640 + -32p) + p(160 + 8p))
p = (-640 + -32p + (160 * p + 8p * p))
p = (-640 + -32p + (160p + 8p2))

Combine like terms: -32p + 160p = 128p
p = (-640 + 128p + 8p2)

Solving
p = -640 + 128p + 8p2

Solving for variable 'p'.

Reorder the terms:
640 + p + -128p + -8p2 = -640 + 128p + 8p2 + 640 + -128p + -8p2

Combine like terms: p + -128p = -127p
640 + -127p + -8p2 = -640 + 128p + 8p2 + 640 + -128p + -8p2

Reorder the terms:
640 + -127p + -8p2 = -640 + 640 + 128p + -128p + 8p2 + -8p2

Combine like terms: -640 + 640 = 0
640 + -127p + -8p2 = 0 + 128p + -128p + 8p2 + -8p2
640 + -127p + -8p2 = 128p + -128p + 8p2 + -8p2

Combine like terms: 128p + -128p = 0
640 + -127p + -8p2 = 0 + 8p2 + -8p2
640 + -127p + -8p2 = 8p2 + -8p2

Combine like terms: 8p2 + -8p2 = 0
640 + -127p + -8p2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-80 + 15.875p + p2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + 15.875p + 80 + p2 = 0 + 80

Reorder the terms:
-80 + 80 + 15.875p + p2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + 15.875p + p2 = 0 + 80
15.875p + p2 = 0 + 80

Combine like terms: 0 + 80 = 80
15.875p + p2 = 80

The p term is 15.875p.  Take half its coefficient (7.9375).
Square it (63.00390625) and add it to both sides.

Add '63.00390625' to each side of the equation.
15.875p + 63.00390625 + p2 = 80 + 63.00390625

Reorder the terms:
63.00390625 + 15.875p + p2 = 80 + 63.00390625

Combine like terms: 80 + 63.00390625 = 143.00390625
63.00390625 + 15.875p + p2 = 143.00390625

Factor a perfect square on the left side:
(p + 7.9375)(p + 7.9375) = 143.00390625

Calculate the square root of the right side: 11.958424071

Break this problem into two subproblems by setting 
(p + 7.9375) equal to 11.958424071 and -11.958424071.

Subproblem 1

p + 7.9375 = 11.958424071 Simplifying p + 7.9375 = 11.958424071 Reorder the terms: 7.9375 + p = 11.958424071 Solving 7.9375 + p = 11.958424071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.9375' to each side of the equation. 7.9375 + -7.9375 + p = 11.958424071 + -7.9375 Combine like terms: 7.9375 + -7.9375 = 0.0000 0.0000 + p = 11.958424071 + -7.9375 p = 11.958424071 + -7.9375 Combine like terms: 11.958424071 + -7.9375 = 4.020924071 p = 4.020924071 Simplifying p = 4.020924071

Subproblem 2

p + 7.9375 = -11.958424071 Simplifying p + 7.9375 = -11.958424071 Reorder the terms: 7.9375 + p = -11.958424071 Solving 7.9375 + p = -11.958424071 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-7.9375' to each side of the equation. 7.9375 + -7.9375 + p = -11.958424071 + -7.9375 Combine like terms: 7.9375 + -7.9375 = 0.0000 0.0000 + p = -11.958424071 + -7.9375 p = -11.958424071 + -7.9375 Combine like terms: -11.958424071 + -7.9375 = -19.895924071 p = -19.895924071 Simplifying p = -19.895924071

Solution

The solution to the problem is based on the solutions from the subproblems. p = {4.020924071, -19.895924071}

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