(3t+1v)(4t-5v)=

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Solution for (3t+1v)(4t-5v)= equation: 


Simplifying
(3t + 1v)(4t + -5v) = 0

Multiply (3t + 1v) * (4t + -5v)
(3t * (4t + -5v) + 1v * (4t + -5v)) = 0
((4t * 3t + -5v * 3t) + 1v * (4t + -5v)) = 0

Reorder the terms:
((-15tv + 12t2) + 1v * (4t + -5v)) = 0
((-15tv + 12t2) + 1v * (4t + -5v)) = 0
(-15tv + 12t2 + (4t * 1v + -5v * 1v)) = 0
(-15tv + 12t2 + (4tv + -5v2)) = 0

Reorder the terms:
(-15tv + 4tv + 12t2 + -5v2) = 0

Combine like terms: -15tv + 4tv = -11tv
(-11tv + 12t2 + -5v2) = 0

Solving
-11tv + 12t2 + -5v2 = 0

Solving for variable 't'.

Factor a trinomial.
(4t + -5v)(3t + v) = 0


Subproblem 1
Set the factor '(4t + -5v)' equal to zero and attempt to solve:

Simplifying
4t + -5v = 0

Solving
4t + -5v = 0

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

Add '5v' to each side of the equation.
4t + -5v + 5v = 0 + 5v

Combine like terms: -5v + 5v = 0
4t + 0 = 0 + 5v
4t = 0 + 5v
Remove the zero:
4t = 5v

Divide each side by '4'.
t = 1.25v

Simplifying
t = 1.25v

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

Simplifying
3t + v = 0

Solving
3t + v = 0

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

Add '-1v' to each side of the equation.
3t + v + -1v = 0 + -1v

Combine like terms: v + -1v = 0
3t + 0 = 0 + -1v
3t = 0 + -1v
Remove the zero:
3t = -1v

Divide each side by '3'.
t = -0.3333333333v

Simplifying
t = -0.3333333333v
Solution
t = {1.25v, -0.3333333333v}

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