R(p)=2.5p^2+500p

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Solution for R(p)=2.5p^2+500p equation: 


Simplifying
R(p) = 2.5p2 + 500p

Multiply R * p
pR = 2.5p2 + 500p

Reorder the terms:
pR = 500p + 2.5p2

Solving
pR = 500p + 2.5p2

Solving for variable 'p'.

Reorder the terms:
-500p + pR + -2.5p2 = 500p + 2.5p2 + -500p + -2.5p2

Reorder the terms:
-500p + pR + -2.5p2 = 500p + -500p + 2.5p2 + -2.5p2

Combine like terms: 500p + -500p = 0
-500p + pR + -2.5p2 = 0 + 2.5p2 + -2.5p2
-500p + pR + -2.5p2 = 2.5p2 + -2.5p2

Combine like terms: 2.5p2 + -2.5p2 = 0.0
-500p + pR + -2.5p2 = 0.0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-500 + R + -2.5p) = 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 '(-500 + R + -2.5p)' equal to zero and attempt to solve:

Simplifying
-500 + R + -2.5p = 0

Solving
-500 + R + -2.5p = 0

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

Add '500' to each side of the equation.
-500 + R + 500 + -2.5p = 0 + 500

Reorder the terms:
-500 + 500 + R + -2.5p = 0 + 500

Combine like terms: -500 + 500 = 0
0 + R + -2.5p = 0 + 500
R + -2.5p = 0 + 500

Combine like terms: 0 + 500 = 500
R + -2.5p = 500

Add '-1R' to each side of the equation.
R + -1R + -2.5p = 500 + -1R

Combine like terms: R + -1R = 0
0 + -2.5p = 500 + -1R
-2.5p = 500 + -1R

Divide each side by '-2.5'.
p = -200 + 0.4R

Simplifying
p = -200 + 0.4R
Solution
p = {0, -200 + 0.4R}

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