5p(p-3q)-2p(2p-5q)-6p(5p+q)=

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Solution for 5p(p-3q)-2p(2p-5q)-6p(5p+q)= equation: 


Simplifying
5p(p + -3q) + -2p(2p + -5q) + -6p(5p + q) = 0
(p * 5p + -3q * 5p) + -2p(2p + -5q) + -6p(5p + q) = 0

Reorder the terms:
(-15pq + 5p2) + -2p(2p + -5q) + -6p(5p + q) = 0
(-15pq + 5p2) + -2p(2p + -5q) + -6p(5p + q) = 0
-15pq + 5p2 + (2p * -2p + -5q * -2p) + -6p(5p + q) = 0

Reorder the terms:
-15pq + 5p2 + (10pq + -4p2) + -6p(5p + q) = 0
-15pq + 5p2 + (10pq + -4p2) + -6p(5p + q) = 0
-15pq + 5p2 + 10pq + -4p2 + (5p * -6p + q * -6p) = 0

Reorder the terms:
-15pq + 5p2 + 10pq + -4p2 + (-6pq + -30p2) = 0
-15pq + 5p2 + 10pq + -4p2 + (-6pq + -30p2) = 0

Reorder the terms:
-15pq + 10pq + -6pq + 5p2 + -4p2 + -30p2 = 0

Combine like terms: -15pq + 10pq = -5pq
-5pq + -6pq + 5p2 + -4p2 + -30p2 = 0

Combine like terms: -5pq + -6pq = -11pq
-11pq + 5p2 + -4p2 + -30p2 = 0

Combine like terms: 5p2 + -4p2 = 1p2
-11pq + 1p2 + -30p2 = 0

Combine like terms: 1p2 + -30p2 = -29p2
-11pq + -29p2 = 0

Solving
-11pq + -29p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '-1p'.
-1p(11q + 29p) = 0

Ignore the factor -1.

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 + 29p)' equal to zero and attempt to solve:

Simplifying
11q + 29p = 0

Reorder the terms:
29p + 11q = 0

Solving
29p + 11q = 0

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

Add '-11q' to each side of the equation.
29p + 11q + -11q = 0 + -11q

Combine like terms: 11q + -11q = 0
29p + 0 = 0 + -11q
29p = 0 + -11q
Remove the zero:
29p = -11q

Divide each side by '29'.
p = -0.3793103448q

Simplifying
p = -0.3793103448q
Solution
p = {0, -0.3793103448q}

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