p(2800-200p)-10(2800-200p)=0

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Solution for p(2800-200p)-10(2800-200p)=0 equation: 


Simplifying
p(2800 + -200p) + -10(2800 + -200p) = 0
(2800 * p + -200p * p) + -10(2800 + -200p) = 0
(2800p + -200p2) + -10(2800 + -200p) = 0
2800p + -200p2 + (2800 * -10 + -200p * -10) = 0
2800p + -200p2 + (-28000 + 2000p) = 0

Reorder the terms:
-28000 + 2800p + 2000p + -200p2 = 0

Combine like terms: 2800p + 2000p = 4800p
-28000 + 4800p + -200p2 = 0

Solving
-28000 + 4800p + -200p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '200'.
200(-140 + 24p + -1p2) = 0

Factor a trinomial.
200((-14 + p)(10 + -1p)) = 0

Ignore the factor 200.

Subproblem 1
Set the factor '(-14 + p)' equal to zero and attempt to solve:

Simplifying
-14 + p = 0

Solving
-14 + p = 0

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

Add '14' to each side of the equation.
-14 + 14 + p = 0 + 14

Combine like terms: -14 + 14 = 0
0 + p = 0 + 14
p = 0 + 14

Combine like terms: 0 + 14 = 14
p = 14

Simplifying
p = 14

Subproblem 2
Set the factor '(10 + -1p)' equal to zero and attempt to solve:

Simplifying
10 + -1p = 0

Solving
10 + -1p = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1p = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1p = 0 + -10
-1p = 0 + -10

Combine like terms: 0 + -10 = -10
-1p = -10

Divide each side by '-1'.
p = 10

Simplifying
p = 10
Solution
p = {14, 10}

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