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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 = -1tSubproblem 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 = 0.3333333333tSolution
m = {-1t, 0.3333333333t}
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