r(p)=-6p^2+42000p

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Solution for r(p)=-6p^2+42000p equation: 


Simplifying
r(p) = -6p2 + 42000p

Multiply r * p
pr = -6p2 + 42000p

Reorder the terms:
pr = 42000p + -6p2

Solving
pr = 42000p + -6p2

Solving for variable 'p'.

Reorder the terms:
-42000p + pr + 6p2 = 42000p + -6p2 + -42000p + 6p2

Reorder the terms:
-42000p + pr + 6p2 = 42000p + -42000p + -6p2 + 6p2

Combine like terms: 42000p + -42000p = 0
-42000p + pr + 6p2 = 0 + -6p2 + 6p2
-42000p + pr + 6p2 = -6p2 + 6p2

Combine like terms: -6p2 + 6p2 = 0
-42000p + pr + 6p2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-42000 + r + 6p) = 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 '(-42000 + r + 6p)' equal to zero and attempt to solve:

Simplifying
-42000 + r + 6p = 0

Reorder the terms:
-42000 + 6p + r = 0

Solving
-42000 + 6p + r = 0

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

Add '42000' to each side of the equation.
-42000 + 6p + 42000 + r = 0 + 42000

Reorder the terms:
-42000 + 42000 + 6p + r = 0 + 42000

Combine like terms: -42000 + 42000 = 0
0 + 6p + r = 0 + 42000
6p + r = 0 + 42000

Combine like terms: 0 + 42000 = 42000
6p + r = 42000

Add '-1r' to each side of the equation.
6p + r + -1r = 42000 + -1r

Combine like terms: r + -1r = 0
6p + 0 = 42000 + -1r
6p = 42000 + -1r

Divide each side by '6'.
p = 7000 + -0.1666666667r

Simplifying
p = 7000 + -0.1666666667r
Solution
p = {0, 7000 + -0.1666666667r}

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