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Simplifying -10t2 + 12t + 54 = 0 Reorder the terms: 54 + 12t + -10t2 = 0 Solving 54 + 12t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 6t + -5t2) = 0 Factor a trinomial. 2((3 + -1t)(9 + 5t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Subproblem 2
Set the factor '(9 + 5t)' equal to zero and attempt to solve: Simplifying 9 + 5t = 0 Solving 9 + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5t = 0 + -9 5t = 0 + -9 Combine like terms: 0 + -9 = -9 5t = -9 Divide each side by '5'. t = -1.8 Simplifying t = -1.8Solution
t = {3, -1.8}
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