4p(2q+3p)+3p(2p+q)=0

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Solution for 4p(2q+3p)+3p(2p+q)=0 equation: 


Simplifying
4p(2q + 3p) + 3p(2p + q) = 0

Reorder the terms:
4p(3p + 2q) + 3p(2p + q) = 0
(3p * 4p + 2q * 4p) + 3p(2p + q) = 0

Reorder the terms:
(8pq + 12p2) + 3p(2p + q) = 0
(8pq + 12p2) + 3p(2p + q) = 0
8pq + 12p2 + (2p * 3p + q * 3p) = 0

Reorder the terms:
8pq + 12p2 + (3pq + 6p2) = 0
8pq + 12p2 + (3pq + 6p2) = 0

Reorder the terms:
8pq + 3pq + 12p2 + 6p2 = 0

Combine like terms: 8pq + 3pq = 11pq
11pq + 12p2 + 6p2 = 0

Combine like terms: 12p2 + 6p2 = 18p2
11pq + 18p2 = 0

Solving
11pq + 18p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), 'p'.
p(11q + 18p) = 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 '(11q + 18p)' equal to zero and attempt to solve:

Simplifying
11q + 18p = 0

Reorder the terms:
18p + 11q = 0

Solving
18p + 11q = 0

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

Add '-11q' to each side of the equation.
18p + 11q + -11q = 0 + -11q

Combine like terms: 11q + -11q = 0
18p + 0 = 0 + -11q
18p = 0 + -11q
Remove the zero:
18p = -11q

Divide each side by '18'.
p = -0.6111111111q

Simplifying
p = -0.6111111111q
Solution
p = {0, -0.6111111111q}

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