12t^2-5tv-2v^2=0

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Solution for 12t^2-5tv-2v^2=0 equation: 


Simplifying
12t2 + -5tv + -2v2 = 0

Reorder the terms:
-5tv + 12t2 + -2v2 = 0

Solving
-5tv + 12t2 + -2v2 = 0

Solving for variable 't'.

Factor a trinomial.
(3t + -2v)(4t + v) = 0


Subproblem 1
Set the factor '(3t + -2v)' equal to zero and attempt to solve:

Simplifying
3t + -2v = 0

Solving
3t + -2v = 0

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

Add '2v' to each side of the equation.
3t + -2v + 2v = 0 + 2v

Combine like terms: -2v + 2v = 0
3t + 0 = 0 + 2v
3t = 0 + 2v
Remove the zero:
3t = 2v

Divide each side by '3'.
t = 0.6666666667v

Simplifying
t = 0.6666666667v

Subproblem 2
Set the factor '(4t + v)' equal to zero and attempt to solve:

Simplifying
4t + v = 0

Solving
4t + v = 0

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

Add '-1v' to each side of the equation.
4t + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
4t + 0 = 0 + -1v
4t = 0 + -1v
Remove the zero:
4t = -1v

Divide each side by '4'.
t = -0.25v

Simplifying
t = -0.25v
Solution
t = {0.6666666667v, -0.25v}

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