6p^4-13p^2q^2+6q^4=0

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Solution for 6p^4-13p^2q^2+6q^4=0 equation: 


Simplifying
6p4 + -13p2q2 + 6q4 = 0

Reorder the terms:
-13p2q2 + 6p4 + 6q4 = 0

Solving
-13p2q2 + 6p4 + 6q4 = 0

Solving for variable 'p'.

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


Subproblem 1
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

Take the square root of each side:
p = {-1.224744871q, 1.224744871q}

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

Simplifying
3p2 + -2q2 = 0

Solving
3p2 + -2q2 = 0

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

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

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

Divide each side by '3'.
p2 = 0.6666666667q2

Simplifying
p2 = 0.6666666667q2

Take the square root of each side:
p = {-0.816496581q, 0.816496581q}
Solution
p = {-1.224744871q, 1.224744871q, -0.816496581q, 0.816496581q}

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