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Simplifying 16t3 + 45t = -56t2 Reorder the terms: 45t + 16t3 = -56t2 Solving 45t + 16t3 = -56t2 Solving for variable 't'. Reorder the terms: 45t + 56t2 + 16t3 = -56t2 + 56t2 Combine like terms: -56t2 + 56t2 = 0 45t + 56t2 + 16t3 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(45 + 56t + 16t2) = 0 Factor a trinomial. t((9 + 4t)(5 + 4t)) = 0Subproblem 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 '(9 + 4t)' equal to zero and attempt to solve: Simplifying 9 + 4t = 0 Solving 9 + 4t = 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 + 4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4t = 0 + -9 4t = 0 + -9 Combine like terms: 0 + -9 = -9 4t = -9 Divide each side by '4'. t = -2.25 Simplifying t = -2.25Subproblem 3
Set the factor '(5 + 4t)' equal to zero and attempt to solve: Simplifying 5 + 4t = 0 Solving 5 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t = 0 + -5 4t = 0 + -5 Combine like terms: 0 + -5 = -5 4t = -5 Divide each side by '4'. t = -1.25 Simplifying t = -1.25Solution
t = {0, -2.25, -1.25}
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