(2m+3t)(3m-4t)=

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Solution for (2m+3t)(3m-4t)= equation: 


Simplifying
(2m + 3t)(3m + -4t) = 0

Multiply (2m + 3t) * (3m + -4t)
(2m * (3m + -4t) + 3t * (3m + -4t)) = 0
((3m * 2m + -4t * 2m) + 3t * (3m + -4t)) = 0

Reorder the terms:
((-8mt + 6m2) + 3t * (3m + -4t)) = 0
((-8mt + 6m2) + 3t * (3m + -4t)) = 0
(-8mt + 6m2 + (3m * 3t + -4t * 3t)) = 0
(-8mt + 6m2 + (9mt + -12t2)) = 0

Reorder the terms:
(-8mt + 9mt + 6m2 + -12t2) = 0

Combine like terms: -8mt + 9mt = 1mt
(1mt + 6m2 + -12t2) = 0

Solving
1mt + 6m2 + -12t2 = 0

Solving for variable 'm'.

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


Subproblem 1
Set the factor '(3m + -4t)' equal to zero and attempt to solve:

Simplifying
3m + -4t = 0

Solving
3m + -4t = 0

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

Add '4t' to each side of the equation.
3m + -4t + 4t = 0 + 4t

Combine like terms: -4t + 4t = 0
3m + 0 = 0 + 4t
3m = 0 + 4t
Remove the zero:
3m = 4t

Divide each side by '3'.
m = 1.333333333t

Simplifying
m = 1.333333333t

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

Simplifying
2m + 3t = 0

Solving
2m + 3t = 0

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

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

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

Divide each side by '2'.
m = -1.5t

Simplifying
m = -1.5t
Solution
m = {1.333333333t, -1.5t}

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