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Simplifying 12t3 + -40t2 + 48t = 0 Reorder the terms: 48t + -40t2 + 12t3 = 0 Solving 48t + -40t2 + 12t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(12 + -10t + 3t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(12 + -10t + 3t2)' equal to zero and attempt to solve: Simplifying 12 + -10t + 3t2 = 0 Solving 12 + -10t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4 + -3.333333333t + t2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3.333333333t + -4 + t2 = 0 + -4 Reorder the terms: 4 + -4 + -3.333333333t + t2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3.333333333t + t2 = 0 + -4 -3.333333333t + t2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3.333333333t + t2 = -4 The t term is -3.333333333t. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333t + 2.777777779 + t2 = -4 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333t + t2 = -4 + 2.777777779 Combine like terms: -4 + 2.777777779 = -1.222222221 2.777777779 + -3.333333333t + t2 = -1.222222221 Factor a perfect square on the left side: (t + -1.666666667)(t + -1.666666667) = -1.222222221 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
t = {0}
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