-6P^2+18000P-1800000=0

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Solution for -6P^2+18000P-1800000=0 equation: 


Simplifying
-6P2 + 18000P + -1800000 = 0

Reorder the terms:
-1800000 + 18000P + -6P2 = 0

Solving
-1800000 + 18000P + -6P2 = 0

Solving for variable 'P'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-300000 + 3000P + -1P2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-300000 + 3000P + -1P2)' equal to zero and attempt to solve:

Simplifying
-300000 + 3000P + -1P2 = 0

Solving
-300000 + 3000P + -1P2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
300000 + -3000P + P2 = 0

Move the constant term to the right:

Add '-300000' to each side of the equation.
300000 + -3000P + -300000 + P2 = 0 + -300000

Reorder the terms:
300000 + -300000 + -3000P + P2 = 0 + -300000

Combine like terms: 300000 + -300000 = 0
0 + -3000P + P2 = 0 + -300000
-3000P + P2 = 0 + -300000

Combine like terms: 0 + -300000 = -300000
-3000P + P2 = -300000

The P term is -3000P.  Take half its coefficient (-1500).
Square it (2250000) and add it to both sides.

Add '2250000' to each side of the equation.
-3000P + 2250000 + P2 = -300000 + 2250000

Reorder the terms:
2250000 + -3000P + P2 = -300000 + 2250000

Combine like terms: -300000 + 2250000 = 1950000
2250000 + -3000P + P2 = 1950000

Factor a perfect square on the left side:
(P + -1500)(P + -1500) = 1950000

Calculate the square root of the right side: 1396.424004377

Break this problem into two subproblems by setting 
(P + -1500) equal to 1396.424004377 and -1396.424004377.


Subproblem 1
P + -1500 = 1396.424004377

Simplifying
P + -1500 = 1396.424004377

Reorder the terms:
-1500 + P = 1396.424004377

Solving
-1500 + P = 1396.424004377

Solving for variable 'P'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + P = 1396.424004377 + 1500

Combine like terms: -1500 + 1500 = 0
0 + P = 1396.424004377 + 1500
P = 1396.424004377 + 1500

Combine like terms: 1396.424004377 + 1500 = 2896.424004377
P = 2896.424004377

Simplifying
P = 2896.424004377


Subproblem 2
P + -1500 = -1396.424004377

Simplifying
P + -1500 = -1396.424004377

Reorder the terms:
-1500 + P = -1396.424004377

Solving
-1500 + P = -1396.424004377

Solving for variable 'P'.

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

Add '1500' to each side of the equation.
-1500 + 1500 + P = -1396.424004377 + 1500

Combine like terms: -1500 + 1500 = 0
0 + P = -1396.424004377 + 1500
P = -1396.424004377 + 1500

Combine like terms: -1396.424004377 + 1500 = 103.575995623
P = 103.575995623

Simplifying
P = 103.575995623


Solution
The solution to the problem is based on the solutions
from the subproblems.
P = {2896.424004377, 103.575995623}
Solution
P = {2896.424004377, 103.575995623}

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