5P(2P+3Q)+2Q(3P+Q)=

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Solution for 5P(2P+3Q)+2Q(3P+Q)= equation: 


Simplifying
5P(2P + 3Q) + 2Q(3P + Q) = 0
(2P * 5P + 3Q * 5P) + 2Q(3P + Q) = 0

Reorder the terms:
(15PQ + 10P2) + 2Q(3P + Q) = 0
(15PQ + 10P2) + 2Q(3P + Q) = 0
15PQ + 10P2 + (3P * 2Q + Q * 2Q) = 0
15PQ + 10P2 + (6PQ + 2Q2) = 0

Reorder the terms:
15PQ + 6PQ + 10P2 + 2Q2 = 0

Combine like terms: 15PQ + 6PQ = 21PQ
21PQ + 10P2 + 2Q2 = 0

Solving
21PQ + 10P2 + 2Q2 = 0

Solving for variable 'P'.

Factor a trinomial.
(10P + Q)(P + 2Q) = 0


Subproblem 1
Set the factor '(10P + Q)' equal to zero and attempt to solve:

Simplifying
10P + Q = 0

Solving
10P + Q = 0

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

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

Combine like terms: Q + -1Q = 0
10P + 0 = 0 + -1Q
10P = 0 + -1Q
Remove the zero:
10P = -1Q

Divide each side by '10'.
P = -0.1Q

Simplifying
P = -0.1Q

Subproblem 2
Set the factor '(P + 2Q)' equal to zero and attempt to solve:

Simplifying
P + 2Q = 0

Solving
P + 2Q = 0

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

Add '-2Q' to each side of the equation.
P + 2Q + -2Q = 0 + -2Q

Combine like terms: 2Q + -2Q = 0
P + 0 = 0 + -2Q
P = 0 + -2Q
Remove the zero:
P = -2Q

Simplifying
P = -2Q
Solution
P = {-0.1Q, -2Q}

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