(3a^2+2b^2)(4a^2-5b^2)=0

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Solution for (3a^2+2b^2)(4a^2-5b^2)=0 equation: 


Simplifying
(3a2 + 2b2)(4a2 + -5b2) = 0

Multiply (3a2 + 2b2) * (4a2 + -5b2)
(3a2 * (4a2 + -5b2) + 2b2 * (4a2 + -5b2)) = 0
((4a2 * 3a2 + -5b2 * 3a2) + 2b2 * (4a2 + -5b2)) = 0

Reorder the terms:
((-15a2b2 + 12a4) + 2b2 * (4a2 + -5b2)) = 0
((-15a2b2 + 12a4) + 2b2 * (4a2 + -5b2)) = 0
(-15a2b2 + 12a4 + (4a2 * 2b2 + -5b2 * 2b2)) = 0
(-15a2b2 + 12a4 + (8a2b2 + -10b4)) = 0

Reorder the terms:
(-15a2b2 + 8a2b2 + 12a4 + -10b4) = 0

Combine like terms: -15a2b2 + 8a2b2 = -7a2b2
(-7a2b2 + 12a4 + -10b4) = 0

Solving
-7a2b2 + 12a4 + -10b4 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a2 + -5b2)(3a2 + 2b2) = 0


Subproblem 1
Set the factor '(4a2 + -5b2)' equal to zero and attempt to solve:

Simplifying
4a2 + -5b2 = 0

Solving
4a2 + -5b2 = 0

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

Add '5b2' to each side of the equation.
4a2 + -5b2 + 5b2 = 0 + 5b2

Combine like terms: -5b2 + 5b2 = 0
4a2 + 0 = 0 + 5b2
4a2 = 0 + 5b2
Remove the zero:
4a2 = 5b2

Divide each side by '4'.
a2 = 1.25b2

Simplifying
a2 = 1.25b2

Take the square root of each side:
a = {-1.118033989b, 1.118033989b}

Subproblem 2
Set the factor '(3a2 + 2b2)' equal to zero and attempt to solve:

Simplifying
3a2 + 2b2 = 0

Solving
3a2 + 2b2 = 0

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

Add '-2b2' to each side of the equation.
3a2 + 2b2 + -2b2 = 0 + -2b2

Combine like terms: 2b2 + -2b2 = 0
3a2 + 0 = 0 + -2b2
3a2 = 0 + -2b2
Remove the zero:
3a2 = -2b2

Divide each side by '3'.
a2 = -0.6666666667b2

Simplifying
a2 = -0.6666666667b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {-1.118033989b, 1.118033989b}

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