20p^4+24p^2q^2-9q^4=0

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Solution for 20p^4+24p^2q^2-9q^4=0 equation: 


Simplifying
20p4 + 24p2q2 + -9q4 = 0

Reorder the terms:
24p2q2 + 20p4 + -9q4 = 0

Solving
24p2q2 + 20p4 + -9q4 = 0

Solving for variable 'p'.

Factor a trinomial.
(10p2 + -3q2)(2p2 + 3q2) = 0


Subproblem 1
Set the factor '(10p2 + -3q2)' equal to zero and attempt to solve:

Simplifying
10p2 + -3q2 = 0

Solving
10p2 + -3q2 = 0

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

Add '3q2' to each side of the equation.
10p2 + -3q2 + 3q2 = 0 + 3q2

Combine like terms: -3q2 + 3q2 = 0
10p2 + 0 = 0 + 3q2
10p2 = 0 + 3q2
Remove the zero:
10p2 = 3q2

Divide each side by '10'.
p2 = 0.3q2

Simplifying
p2 = 0.3q2

Take the square root of each side:
p = {-0.547722558q, 0.547722558q}

Subproblem 2
Set the factor '(2p2 + 3q2)' equal to zero and attempt to solve:

Simplifying
2p2 + 3q2 = 0

Solving
2p2 + 3q2 = 0

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

Add '-3q2' to each side of the equation.
2p2 + 3q2 + -3q2 = 0 + -3q2

Combine like terms: 3q2 + -3q2 = 0
2p2 + 0 = 0 + -3q2
2p2 = 0 + -3q2
Remove the zero:
2p2 = -3q2

Divide each side by '2'.
p2 = -1.5q2

Simplifying
p2 = -1.5q2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
p = {-0.547722558q, 0.547722558q}

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