(6t^2-8bs)(t^2+bs)=

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Solution for (6t^2-8bs)(t^2+bs)= equation: 


Simplifying
(6t2 + -8bs)(t2 + bs) = 0

Reorder the terms:
(-8bs + 6t2)(t2 + bs) = 0

Reorder the terms:
(-8bs + 6t2)(bs + t2) = 0

Multiply (-8bs + 6t2) * (bs + t2)
(-8bs * (bs + t2) + 6t2 * (bs + t2)) = 0
((bs * -8bs + t2 * -8bs) + 6t2 * (bs + t2)) = 0

Reorder the terms:
((-8bst2 + -8b2s2) + 6t2 * (bs + t2)) = 0
((-8bst2 + -8b2s2) + 6t2 * (bs + t2)) = 0
(-8bst2 + -8b2s2 + (bs * 6t2 + t2 * 6t2)) = 0
(-8bst2 + -8b2s2 + (6bst2 + 6t4)) = 0

Reorder the terms:
(-8bst2 + 6bst2 + -8b2s2 + 6t4) = 0

Combine like terms: -8bst2 + 6bst2 = -2bst2
(-2bst2 + -8b2s2 + 6t4) = 0

Solving
-2bst2 + -8b2s2 + 6t4 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1bst2 + -4b2s2 + 3t4) = 0

Factor a trinomial.
2((-1bs + -1t2)(4bs + -3t2)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-1bs + -1t2)' equal to zero and attempt to solve:

Simplifying
-1bs + -1t2 = 0

Solving
-1bs + -1t2 = 0

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

Add 't2' to each side of the equation.
-1bs + -1t2 + t2 = 0 + t2

Combine like terms: -1t2 + t2 = 0
-1bs + 0 = 0 + t2
-1bs = 0 + t2
Remove the zero:
-1bs = t2

Divide each side by '-1s'.
b = -1s-1t2

Simplifying
b = -1s-1t2

Subproblem 2
Set the factor '(4bs + -3t2)' equal to zero and attempt to solve:

Simplifying
4bs + -3t2 = 0

Solving
4bs + -3t2 = 0

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

Add '3t2' to each side of the equation.
4bs + -3t2 + 3t2 = 0 + 3t2

Combine like terms: -3t2 + 3t2 = 0
4bs + 0 = 0 + 3t2
4bs = 0 + 3t2
Remove the zero:
4bs = 3t2

Divide each side by '4s'.
b = 0.75s-1t2

Simplifying
b = 0.75s-1t2
Solution
b = {-1s-1t2, 0.75s-1t2}

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