R(p)=5p(p-84)

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Solution for R(p)=5p(p-84) equation: 


Simplifying
R(p) = 5p(p + -84)

Multiply R * p
pR = 5p(p + -84)

Reorder the terms:
pR = 5p(-84 + p)
pR = (-84 * 5p + p * 5p)
pR = (-420p + 5p2)

Solving
pR = -420p + 5p2

Solving for variable 'p'.

Reorder the terms:
420p + pR + -5p2 = -420p + 5p2 + 420p + -5p2

Reorder the terms:
420p + pR + -5p2 = -420p + 420p + 5p2 + -5p2

Combine like terms: -420p + 420p = 0
420p + pR + -5p2 = 0 + 5p2 + -5p2
420p + pR + -5p2 = 5p2 + -5p2

Combine like terms: 5p2 + -5p2 = 0
420p + pR + -5p2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(420 + R + -5p) = 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 '(420 + R + -5p)' equal to zero and attempt to solve:

Simplifying
420 + R + -5p = 0

Solving
420 + R + -5p = 0

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

Add '-420' to each side of the equation.
420 + R + -420 + -5p = 0 + -420

Reorder the terms:
420 + -420 + R + -5p = 0 + -420

Combine like terms: 420 + -420 = 0
0 + R + -5p = 0 + -420
R + -5p = 0 + -420

Combine like terms: 0 + -420 = -420
R + -5p = -420

Add '-1R' to each side of the equation.
R + -1R + -5p = -420 + -1R

Combine like terms: R + -1R = 0
0 + -5p = -420 + -1R
-5p = -420 + -1R

Divide each side by '-5'.
p = 84 + 0.2R

Simplifying
p = 84 + 0.2R
Solution
p = {0, 84 + 0.2R}

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