(s^2+bu)(2s^2+3bu)=0

Solution for (s^2+bu)(2s^2+3bu)=0 equation:

Simplifying
(s2 + bu)(2s2 + 3bu) = 0

Reorder the terms:
(bu + s2)(2s2 + 3bu) = 0

Reorder the terms:
(bu + s2)(3bu + 2s2) = 0

Multiply (bu + s2) * (3bu + 2s2)
(bu(3bu + 2s2) + s2(3bu + 2s2)) = 0
((3bu * bu + 2s2 * bu) + s2(3bu + 2s2)) = 0

Reorder the terms:
((2bs2u + 3b2u2) + s2(3bu + 2s2)) = 0
((2bs2u + 3b2u2) + s2(3bu + 2s2)) = 0
(2bs2u + 3b2u2 + (3bu * s2 + 2s2 * s2)) = 0
(2bs2u + 3b2u2 + (3bs2u + 2s4)) = 0

Reorder the terms:
(2bs2u + 3bs2u + 3b2u2 + 2s4) = 0

Combine like terms: 2bs2u + 3bs2u = 5bs2u
(5bs2u + 3b2u2 + 2s4) = 0

Solving
5bs2u + 3b2u2 + 2s4 = 0

Solving for variable 'b'.

Factor a trinomial.
(3bu + 2s2)(bu + s2) = 0

Subproblem 1
Set the factor '(3bu + 2s2)' equal to zero and attempt to solve:

Simplifying
3bu + 2s2 = 0

Solving
3bu + 2s2 = 0

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

Add '-2s2' to each side of the equation.
3bu + 2s2 + -2s2 = 0 + -2s2

Combine like terms: 2s2 + -2s2 = 0
3bu + 0 = 0 + -2s2
3bu = 0 + -2s2
Remove the zero:
3bu = -2s2

Divide each side by '3u'.
b = -0.6666666667s2u-1

Simplifying
b = -0.6666666667s2u-1
Subproblem 2
Set the factor '(bu + s2)' equal to zero and attempt to solve:

Simplifying
bu + s2 = 0

Solving
bu + s2 = 0

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

Add '-1s2' to each side of the equation.
bu + s2 + -1s2 = 0 + -1s2

Combine like terms: s2 + -1s2 = 0
bu + 0 = 0 + -1s2
bu = 0 + -1s2
Remove the zero:
bu = -1s2

Divide each side by 'u'.
b = -1s2u-1

Simplifying
b = -1s2u-1
Solution
b = {-0.6666666667s2u-1, -1s2u-1}