4p^2(-2q^2+1)-2p(2q^2-1)=0

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Solution for 4p^2(-2q^2+1)-2p(2q^2-1)=0 equation: 


Simplifying
4p2(-2q2 + 1) + -2p(2q2 + -1) = 0

Reorder the terms:
4p2(1 + -2q2) + -2p(2q2 + -1) = 0
(1 * 4p2 + -2q2 * 4p2) + -2p(2q2 + -1) = 0
(4p2 + -8p2q2) + -2p(2q2 + -1) = 0

Reorder the terms:
4p2 + -8p2q2 + -2p(-1 + 2q2) = 0
4p2 + -8p2q2 + (-1 * -2p + 2q2 * -2p) = 0
4p2 + -8p2q2 + (2p + -4pq2) = 0

Reorder the terms:
2p + -4pq2 + 4p2 + -8p2q2 = 0

Solving
2p + -4pq2 + 4p2 + -8p2q2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2p'.
2p(1 + -2q2 + 2p + -4pq2) = 0

Ignore the factor 2.

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 '(1 + -2q2 + 2p + -4pq2)' equal to zero and attempt to solve:

Simplifying
1 + -2q2 + 2p + -4pq2 = 0

Reorder the terms:
1 + 2p + -4pq2 + -2q2 = 0

Solving
1 + 2p + -4pq2 + -2q2 = 0

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

Add '-1' to each side of the equation.
1 + 2p + -4pq2 + -1 + -2q2 = 0 + -1

Reorder the terms:
1 + -1 + 2p + -4pq2 + -2q2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2p + -4pq2 + -2q2 = 0 + -1
2p + -4pq2 + -2q2 = 0 + -1

Combine like terms: 0 + -1 = -1
2p + -4pq2 + -2q2 = -1

Add '2q2' to each side of the equation.
2p + -4pq2 + -2q2 + 2q2 = -1 + 2q2

Combine like terms: -2q2 + 2q2 = 0
2p + -4pq2 + 0 = -1 + 2q2
2p + -4pq2 = -1 + 2q2

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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