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Simplifying 72 = 9t2 + -12t + 60 Reorder the terms: 72 = 60 + -12t + 9t2 Solving 72 = 60 + -12t + 9t2 Solving for variable 't'. Combine like terms: 72 + -60 = 12 12 + 12t + -9t2 = 60 + -12t + 9t2 + -60 + 12t + -9t2 Reorder the terms: 12 + 12t + -9t2 = 60 + -60 + -12t + 12t + 9t2 + -9t2 Combine like terms: 60 + -60 = 0 12 + 12t + -9t2 = 0 + -12t + 12t + 9t2 + -9t2 12 + 12t + -9t2 = -12t + 12t + 9t2 + -9t2 Combine like terms: -12t + 12t = 0 12 + 12t + -9t2 = 0 + 9t2 + -9t2 12 + 12t + -9t2 = 9t2 + -9t2 Combine like terms: 9t2 + -9t2 = 0 12 + 12t + -9t2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 4t + -3t2) = 0 Factor a trinomial. 3((2 + -1t)(2 + 3t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(2 + 3t)' equal to zero and attempt to solve: Simplifying 2 + 3t = 0 Solving 2 + 3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3t = 0 + -2 3t = 0 + -2 Combine like terms: 0 + -2 = -2 3t = -2 Divide each side by '3'. t = -0.6666666667 Simplifying t = -0.6666666667Solution
t = {2, -0.6666666667}
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