(b-3tv^2)(2b-tv^2)=0

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Solution for (b-3tv^2)(2b-tv^2)=0 equation: 


Simplifying
(b + -3tv2)(2b + -1tv2) = 0

Multiply (b + -3tv2) * (2b + -1tv2)
(b(2b + -1tv2) + -3tv2 * (2b + -1tv2)) = 0
((2b * b + -1tv2 * b) + -3tv2 * (2b + -1tv2)) = 0

Reorder the terms:
((-1btv2 + 2b2) + -3tv2 * (2b + -1tv2)) = 0
((-1btv2 + 2b2) + -3tv2 * (2b + -1tv2)) = 0
(-1btv2 + 2b2 + (2b * -3tv2 + -1tv2 * -3tv2)) = 0
(-1btv2 + 2b2 + (-6btv2 + 3t2v4)) = 0

Reorder the terms:
(-1btv2 + -6btv2 + 2b2 + 3t2v4) = 0

Combine like terms: -1btv2 + -6btv2 = -7btv2
(-7btv2 + 2b2 + 3t2v4) = 0

Solving
-7btv2 + 2b2 + 3t2v4 = 0

Solving for variable 'b'.

Factor a trinomial.
(b + -3tv2)(2b + -1tv2) = 0


Subproblem 1
Set the factor '(b + -3tv2)' equal to zero and attempt to solve:

Simplifying
b + -3tv2 = 0

Solving
b + -3tv2 = 0

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

Add '3tv2' to each side of the equation.
b + -3tv2 + 3tv2 = 0 + 3tv2

Combine like terms: -3tv2 + 3tv2 = 0
b + 0 = 0 + 3tv2
b = 0 + 3tv2
Remove the zero:
b = 3tv2

Simplifying
b = 3tv2

Subproblem 2
Set the factor '(2b + -1tv2)' equal to zero and attempt to solve:

Simplifying
2b + -1tv2 = 0

Solving
2b + -1tv2 = 0

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

Add 'tv2' to each side of the equation.
2b + -1tv2 + tv2 = 0 + tv2

Combine like terms: -1tv2 + tv2 = 0
2b + 0 = 0 + tv2
2b = 0 + tv2
Remove the zero:
2b = tv2

Divide each side by '2'.
b = 0.5tv2

Simplifying
b = 0.5tv2
Solution
b = {3tv2, 0.5tv2}

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