4px^2-p^2q^2=2pqx-2p^2q

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Solution for 4px^2-p^2q^2=2pqx-2p^2q equation: 


Simplifying
4px2 + -1p2q2 = 2pqx + -2p2q

Solving
4px2 + -1p2q2 = 2pqx + -2p2q

Solving for variable 'p'.

Reorder the terms:
-2pqx + 4px2 + 2p2q + -1p2q2 = 2pqx + -2p2q + -2pqx + 2p2q

Reorder the terms:
-2pqx + 4px2 + 2p2q + -1p2q2 = 2pqx + -2pqx + -2p2q + 2p2q

Combine like terms: 2pqx + -2pqx = 0
-2pqx + 4px2 + 2p2q + -1p2q2 = 0 + -2p2q + 2p2q
-2pqx + 4px2 + 2p2q + -1p2q2 = -2p2q + 2p2q

Combine like terms: -2p2q + 2p2q = 0
-2pqx + 4px2 + 2p2q + -1p2q2 = 0

Factor out the Greatest Common Factor (GCF), 'p'.
p(-2qx + 4x2 + 2pq + -1pq2) = 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 '(-2qx + 4x2 + 2pq + -1pq2)' equal to zero and attempt to solve:

Simplifying
-2qx + 4x2 + 2pq + -1pq2 = 0

Reorder the terms:
2pq + -1pq2 + -2qx + 4x2 = 0

Solving
2pq + -1pq2 + -2qx + 4x2 = 0

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

Add '2qx' to each side of the equation.
2pq + -1pq2 + -2qx + 2qx + 4x2 = 0 + 2qx

Combine like terms: -2qx + 2qx = 0
2pq + -1pq2 + 0 + 4x2 = 0 + 2qx
2pq + -1pq2 + 4x2 = 0 + 2qx
Remove the zero:
2pq + -1pq2 + 4x2 = 2qx

Add '-4x2' to each side of the equation.
2pq + -1pq2 + 4x2 + -4x2 = 2qx + -4x2

Combine like terms: 4x2 + -4x2 = 0
2pq + -1pq2 + 0 = 2qx + -4x2
2pq + -1pq2 = 2qx + -4x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {0}

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