(x^2+bn)(2x^2+3bn)=0

Solution for (x^2+bn)(2x^2+3bn)=0 equation:

Simplifying
(x2 + bn)(2x2 + 3bn) = 0

Reorder the terms:
(bn + x2)(2x2 + 3bn) = 0

Reorder the terms:
(bn + x2)(3bn + 2x2) = 0

Multiply (bn + x2) * (3bn + 2x2)
(bn(3bn + 2x2) + x2(3bn + 2x2)) = 0
((3bn * bn + 2x2 * bn) + x2(3bn + 2x2)) = 0

Reorder the terms:
((2bnx2 + 3b2n2) + x2(3bn + 2x2)) = 0
((2bnx2 + 3b2n2) + x2(3bn + 2x2)) = 0
(2bnx2 + 3b2n2 + (3bn * x2 + 2x2 * x2)) = 0
(2bnx2 + 3b2n2 + (3bnx2 + 2x4)) = 0

Reorder the terms:
(2bnx2 + 3bnx2 + 3b2n2 + 2x4) = 0

Combine like terms: 2bnx2 + 3bnx2 = 5bnx2
(5bnx2 + 3b2n2 + 2x4) = 0

Solving
5bnx2 + 3b2n2 + 2x4 = 0

Solving for variable 'b'.

Factor a trinomial.
(3bn + 2x2)(bn + x2) = 0

Subproblem 1
Set the factor '(3bn + 2x2)' equal to zero and attempt to solve:

Simplifying
3bn + 2x2 = 0

Solving
3bn + 2x2 = 0

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

Add '-2x2' to each side of the equation.
3bn + 2x2 + -2x2 = 0 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3bn + 0 = 0 + -2x2
3bn = 0 + -2x2
Remove the zero:
3bn = -2x2

Divide each side by '3n'.
b = -0.6666666667n-1x2

Simplifying
b = -0.6666666667n-1x2
Subproblem 2
Set the factor '(bn + x2)' equal to zero and attempt to solve:

Simplifying
bn + x2 = 0

Solving
bn + x2 = 0

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

Add '-1x2' to each side of the equation.
bn + x2 + -1x2 = 0 + -1x2

Combine like terms: x2 + -1x2 = 0
bn + 0 = 0 + -1x2
bn = 0 + -1x2
Remove the zero:
bn = -1x2

Divide each side by 'n'.
b = -1n-1x2

Simplifying
b = -1n-1x2
Solution
b = {-0.6666666667n-1x2, -1n-1x2}