(2a-sb)(3a+4sb)=0

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Solution for (2a-sb)(3a+4sb)=0 equation: 


Simplifying
(2a + -1sb)(3a + 4sb) = 0

Multiply (2a + -1bs) * (3a + 4bs)
(2a * (3a + 4bs) + -1bs * (3a + 4bs)) = 0
((3a * 2a + 4bs * 2a) + -1bs * (3a + 4bs)) = 0

Reorder the terms:
((8abs + 6a2) + -1bs * (3a + 4bs)) = 0
((8abs + 6a2) + -1bs * (3a + 4bs)) = 0
(8abs + 6a2 + (3a * -1bs + 4bs * -1bs)) = 0
(8abs + 6a2 + (-3abs + -4b2s2)) = 0

Reorder the terms:
(8abs + -3abs + 6a2 + -4b2s2) = 0

Combine like terms: 8abs + -3abs = 5abs
(5abs + 6a2 + -4b2s2) = 0

Solving
5abs + 6a2 + -4b2s2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -1bs)(3a + 4bs) = 0


Subproblem 1
Set the factor '(2a + -1bs)' equal to zero and attempt to solve:

Simplifying
2a + -1bs = 0

Solving
2a + -1bs = 0

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

Add 'bs' to each side of the equation.
2a + -1bs + bs = 0 + bs

Combine like terms: -1bs + bs = 0
2a + 0 = 0 + bs
2a = 0 + bs
Remove the zero:
2a = bs

Divide each side by '2'.
a = 0.5bs

Simplifying
a = 0.5bs

Subproblem 2
Set the factor '(3a + 4bs)' equal to zero and attempt to solve:

Simplifying
3a + 4bs = 0

Solving
3a + 4bs = 0

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

Add '-4bs' to each side of the equation.
3a + 4bs + -4bs = 0 + -4bs

Combine like terms: 4bs + -4bs = 0
3a + 0 = 0 + -4bs
3a = 0 + -4bs
Remove the zero:
3a = -4bs

Divide each side by '3'.
a = -1.333333333bs

Simplifying
a = -1.333333333bs
Solution
a = {0.5bs, -1.333333333bs}

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