12t(t+m)(t-3m)=0

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Solution for 12t(t+m)(t-3m)=0 equation: 


Simplifying
12t(t + m)(t + -3m) = 0

Reorder the terms:
12t(m + t)(t + -3m) = 0

Reorder the terms:
12t(m + t)(-3m + t) = 0

Multiply (m + t) * (-3m + t)
12t(m(-3m + t) + t(-3m + t)) = 0
12t((-3m * m + t * m) + t(-3m + t)) = 0

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

Reorder the terms:
12t(mt + -3mt + -3m2 + t2) = 0

Combine like terms: mt + -3mt = -2mt
12t(-2mt + -3m2 + t2) = 0
(-2mt * 12t + -3m2 * 12t + t2 * 12t) = 0
(-24mt2 + -36m2t + 12t3) = 0

Solving
-24mt2 + -36m2t + 12t3 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '12t'.
12t(-2mt + -3m2 + t2) = 0

Factor a trinomial.
12t((-1m + -1t)(3m + -1t)) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 't' equal to zero and attempt to solve:

Simplifying
t = 0

Solving
t = 0

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

Add '-1t' to each side of the equation.
t + -1t = 0 + -1t
Remove the zero:
0 = -1t

Simplifying
0 = -1t

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
-1m + -1t = 0

Solving
-1m + -1t = 0

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

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

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

Divide each side by '-1'.
m = -1t

Simplifying
m = -1t

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

Simplifying
3m + -1t = 0

Solving
3m + -1t = 0

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

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

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

Divide each side by '3'.
m = 0.3333333333t

Simplifying
m = 0.3333333333t
Solution
m = {-1t, 0.3333333333t}

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