80p-4p^2=20p+150

Solution for 80p-4p^2=20p+150 equation:

Simplifying
80p + -4p2 = 20p + 150

Reorder the terms:
80p + -4p2 = 150 + 20p

Solving
80p + -4p2 = 150 + 20p

Solving for variable 'p'.

Reorder the terms:
-150 + 80p + -20p + -4p2 = 150 + 20p + -150 + -20p

Combine like terms: 80p + -20p = 60p
-150 + 60p + -4p2 = 150 + 20p + -150 + -20p

Reorder the terms:
-150 + 60p + -4p2 = 150 + -150 + 20p + -20p

Combine like terms: 150 + -150 = 0
-150 + 60p + -4p2 = 0 + 20p + -20p
-150 + 60p + -4p2 = 20p + -20p

Combine like terms: 20p + -20p = 0
-150 + 60p + -4p2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + 30p + -2p2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-75 + 30p + -2p2)' equal to zero and attempt to solve:

Simplifying
-75 + 30p + -2p2 = 0

Solving
-75 + 30p + -2p2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
37.5 + -15p + p2 = 0

Move the constant term to the right:

Add '-37.5' to each side of the equation.
37.5 + -15p + -37.5 + p2 = 0 + -37.5

Reorder the terms:
37.5 + -37.5 + -15p + p2 = 0 + -37.5

Combine like terms: 37.5 + -37.5 = 0.0
0.0 + -15p + p2 = 0 + -37.5
-15p + p2 = 0 + -37.5

Combine like terms: 0 + -37.5 = -37.5
-15p + p2 = -37.5

The p term is -15p.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15p + 56.25 + p2 = -37.5 + 56.25

Reorder the terms:
56.25 + -15p + p2 = -37.5 + 56.25

Combine like terms: -37.5 + 56.25 = 18.75
56.25 + -15p + p2 = 18.75

Factor a perfect square on the left side:
(p + -7.5)(p + -7.5) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(p + -7.5) equal to 4.330127019 and -4.330127019.

Subproblem 1
p + -7.5 = 4.330127019

Simplifying
p + -7.5 = 4.330127019

Reorder the terms:
-7.5 + p = 4.330127019

Solving
-7.5 + p = 4.330127019

Solving for variable 'p'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + p = 4.330127019 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + p = 4.330127019 + 7.5
p = 4.330127019 + 7.5

Combine like terms: 4.330127019 + 7.5 = 11.830127019
p = 11.830127019

Simplifying
p = 11.830127019

Subproblem 2
p + -7.5 = -4.330127019

Simplifying
p + -7.5 = -4.330127019

Reorder the terms:
-7.5 + p = -4.330127019

Solving
-7.5 + p = -4.330127019

Solving for variable 'p'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + p = -4.330127019 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + p = -4.330127019 + 7.5
p = -4.330127019 + 7.5

Combine like terms: -4.330127019 + 7.5 = 3.169872981
p = 3.169872981

Simplifying
p = 3.169872981

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {11.830127019, 3.169872981}
Solution
p = {11.830127019, 3.169872981}