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

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


Simplifying
4(2p + 3q)(2p + 3q) + -1(3p + -1q)(3p + -1q) = 0

Multiply (2p + 3q) * (2p + 3q)
4(2p * (2p + 3q) + 3q * (2p + 3q)) + -1(3p + -1q)(3p + -1q) = 0
4((2p * 2p + 3q * 2p) + 3q * (2p + 3q)) + -1(3p + -1q)(3p + -1q) = 0

Reorder the terms:
4((6pq + 4p2) + 3q * (2p + 3q)) + -1(3p + -1q)(3p + -1q) = 0
4((6pq + 4p2) + 3q * (2p + 3q)) + -1(3p + -1q)(3p + -1q) = 0
4(6pq + 4p2 + (2p * 3q + 3q * 3q)) + -1(3p + -1q)(3p + -1q) = 0
4(6pq + 4p2 + (6pq + 9q2)) + -1(3p + -1q)(3p + -1q) = 0

Reorder the terms:
4(6pq + 6pq + 4p2 + 9q2) + -1(3p + -1q)(3p + -1q) = 0

Combine like terms: 6pq + 6pq = 12pq
4(12pq + 4p2 + 9q2) + -1(3p + -1q)(3p + -1q) = 0
(12pq * 4 + 4p2 * 4 + 9q2 * 4) + -1(3p + -1q)(3p + -1q) = 0
(48pq + 16p2 + 36q2) + -1(3p + -1q)(3p + -1q) = 0

Multiply (3p + -1q) * (3p + -1q)
48pq + 16p2 + 36q2 + -1(3p * (3p + -1q) + -1q * (3p + -1q)) = 0
48pq + 16p2 + 36q2 + -1((3p * 3p + -1q * 3p) + -1q * (3p + -1q)) = 0

Reorder the terms:
48pq + 16p2 + 36q2 + -1((-3pq + 9p2) + -1q * (3p + -1q)) = 0
48pq + 16p2 + 36q2 + -1((-3pq + 9p2) + -1q * (3p + -1q)) = 0
48pq + 16p2 + 36q2 + -1(-3pq + 9p2 + (3p * -1q + -1q * -1q)) = 0
48pq + 16p2 + 36q2 + -1(-3pq + 9p2 + (-3pq + 1q2)) = 0

Reorder the terms:
48pq + 16p2 + 36q2 + -1(-3pq + -3pq + 9p2 + 1q2) = 0

Combine like terms: -3pq + -3pq = -6pq
48pq + 16p2 + 36q2 + -1(-6pq + 9p2 + 1q2) = 0
48pq + 16p2 + 36q2 + (-6pq * -1 + 9p2 * -1 + 1q2 * -1) = 0
48pq + 16p2 + 36q2 + (6pq + -9p2 + -1q2) = 0

Reorder the terms:
48pq + 6pq + 16p2 + -9p2 + 36q2 + -1q2 = 0

Combine like terms: 48pq + 6pq = 54pq
54pq + 16p2 + -9p2 + 36q2 + -1q2 = 0

Combine like terms: 16p2 + -9p2 = 7p2
54pq + 7p2 + 36q2 + -1q2 = 0

Combine like terms: 36q2 + -1q2 = 35q2
54pq + 7p2 + 35q2 = 0

Solving
54pq + 7p2 + 35q2 = 0

Solving for variable 'p'.

Factor a trinomial.
(7p + 5q)(p + 7q) = 0


Subproblem 1
Set the factor '(7p + 5q)' equal to zero and attempt to solve:

Simplifying
7p + 5q = 0

Solving
7p + 5q = 0

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

Add '-5q' to each side of the equation.
7p + 5q + -5q = 0 + -5q

Combine like terms: 5q + -5q = 0
7p + 0 = 0 + -5q
7p = 0 + -5q
Remove the zero:
7p = -5q

Divide each side by '7'.
p = -0.7142857143q

Simplifying
p = -0.7142857143q

Subproblem 2
Set the factor '(p + 7q)' equal to zero and attempt to solve:

Simplifying
p + 7q = 0

Solving
p + 7q = 0

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

Add '-7q' to each side of the equation.
p + 7q + -7q = 0 + -7q

Combine like terms: 7q + -7q = 0
p + 0 = 0 + -7q
p = 0 + -7q
Remove the zero:
p = -7q

Simplifying
p = -7q
Solution
p = {-0.7142857143q, -7q}

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