-12p^4+14p^2q^2+40q^4=0

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Solution for -12p^4+14p^2q^2+40q^4=0 equation: 


Simplifying
-12p4 + 14p2q2 + 40q4 = 0

Reorder the terms:
14p2q2 + -12p4 + 40q4 = 0

Solving
14p2q2 + -12p4 + 40q4 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7p2q2 + -6p4 + 20q4) = 0

Factor a trinomial.
2((-3p2 + -4q2)(2p2 + -5q2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3p2 + -4q2)' equal to zero and attempt to solve:

Simplifying
-3p2 + -4q2 = 0

Solving
-3p2 + -4q2 = 0

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

Add '4q2' to each side of the equation.
-3p2 + -4q2 + 4q2 = 0 + 4q2

Combine like terms: -4q2 + 4q2 = 0
-3p2 + 0 = 0 + 4q2
-3p2 = 0 + 4q2
Remove the zero:
-3p2 = 4q2

Divide each side by '-3'.
p2 = -1.333333333q2

Simplifying
p2 = -1.333333333q2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(2p2 + -5q2)' equal to zero and attempt to solve:

Simplifying
2p2 + -5q2 = 0

Solving
2p2 + -5q2 = 0

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

Add '5q2' to each side of the equation.
2p2 + -5q2 + 5q2 = 0 + 5q2

Combine like terms: -5q2 + 5q2 = 0
2p2 + 0 = 0 + 5q2
2p2 = 0 + 5q2
Remove the zero:
2p2 = 5q2

Divide each side by '2'.
p2 = 2.5q2

Simplifying
p2 = 2.5q2

Take the square root of each side:
p = {-1.58113883q, 1.58113883q}
Solution
p = {-1.58113883q, 1.58113883q}

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