R(P)=100P-0.2P^2

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Solution for R(P)=100P-0.2P^2 equation: 


Simplifying
R(P) = 100P + -0.2P2

Multiply R * P
PR = 100P + -0.2P2

Solving
PR = 100P + -0.2P2

Solving for variable 'P'.

Reorder the terms:
-100P + PR + 0.2P2 = 100P + -0.2P2 + -100P + 0.2P2

Reorder the terms:
-100P + PR + 0.2P2 = 100P + -100P + -0.2P2 + 0.2P2

Combine like terms: 100P + -100P = 0
-100P + PR + 0.2P2 = 0 + -0.2P2 + 0.2P2
-100P + PR + 0.2P2 = -0.2P2 + 0.2P2

Combine like terms: -0.2P2 + 0.2P2 = 0.0
-100P + PR + 0.2P2 = 0.0

Factor out the Greatest Common Factor (GCF), 'P'.
P(-100 + R + 0.2P) = 0.0


Subproblem 1
Set the factor 'P' equal to zero and attempt to solve:

Simplifying
P = 0

Solving
P = 0

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

Simplifying
P = 0

Subproblem 2
Set the factor '(-100 + R + 0.2P)' equal to zero and attempt to solve:

Simplifying
-100 + R + 0.2P = 0

Reorder the terms:
-100 + 0.2P + R = 0

Solving
-100 + 0.2P + R = 0

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

Add '100' to each side of the equation.
-100 + 0.2P + 100 + R = 0 + 100

Reorder the terms:
-100 + 100 + 0.2P + R = 0 + 100

Combine like terms: -100 + 100 = 0
0 + 0.2P + R = 0 + 100
0.2P + R = 0 + 100

Combine like terms: 0 + 100 = 100
0.2P + R = 100

Add '-1R' to each side of the equation.
0.2P + R + -1R = 100 + -1R

Combine like terms: R + -1R = 0
0.2P + 0 = 100 + -1R
0.2P = 100 + -1R

Divide each side by '0.2'.
P = 500 + -5R

Simplifying
P = 500 + -5R
Solution
P = {0, 500 + -5R}

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