(2v^2+3bt)(3v^2-bt)=

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Solution for (2v^2+3bt)(3v^2-bt)= equation: 


Simplifying
(2v2 + 3bt)(3v2 + -1bt) = 0

Reorder the terms:
(3bt + 2v2)(3v2 + -1bt) = 0

Reorder the terms:
(3bt + 2v2)(-1bt + 3v2) = 0

Multiply (3bt + 2v2) * (-1bt + 3v2)
(3bt * (-1bt + 3v2) + 2v2 * (-1bt + 3v2)) = 0
((-1bt * 3bt + 3v2 * 3bt) + 2v2 * (-1bt + 3v2)) = 0

Reorder the terms:
((9btv2 + -3b2t2) + 2v2 * (-1bt + 3v2)) = 0
((9btv2 + -3b2t2) + 2v2 * (-1bt + 3v2)) = 0
(9btv2 + -3b2t2 + (-1bt * 2v2 + 3v2 * 2v2)) = 0
(9btv2 + -3b2t2 + (-2btv2 + 6v4)) = 0

Reorder the terms:
(9btv2 + -2btv2 + -3b2t2 + 6v4) = 0

Combine like terms: 9btv2 + -2btv2 = 7btv2
(7btv2 + -3b2t2 + 6v4) = 0

Solving
7btv2 + -3b2t2 + 6v4 = 0

Solving for variable 'b'.

Factor a trinomial.
(-3bt + -2v2)(bt + -3v2) = 0


Subproblem 1
Set the factor '(-3bt + -2v2)' equal to zero and attempt to solve:

Simplifying
-3bt + -2v2 = 0

Solving
-3bt + -2v2 = 0

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

Add '2v2' to each side of the equation.
-3bt + -2v2 + 2v2 = 0 + 2v2

Combine like terms: -2v2 + 2v2 = 0
-3bt + 0 = 0 + 2v2
-3bt = 0 + 2v2
Remove the zero:
-3bt = 2v2

Divide each side by '-3t'.
b = -0.6666666667t-1v2

Simplifying
b = -0.6666666667t-1v2

Subproblem 2
Set the factor '(bt + -3v2)' equal to zero and attempt to solve:

Simplifying
bt + -3v2 = 0

Solving
bt + -3v2 = 0

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

Add '3v2' to each side of the equation.
bt + -3v2 + 3v2 = 0 + 3v2

Combine like terms: -3v2 + 3v2 = 0
bt + 0 = 0 + 3v2
bt = 0 + 3v2
Remove the zero:
bt = 3v2

Divide each side by 't'.
b = 3t-1v2

Simplifying
b = 3t-1v2
Solution
b = {-0.6666666667t-1v2, 3t-1v2}

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