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Simplifying -2t2 = 108t + -30t2 Solving -2t2 = 108t + -30t2 Solving for variable 't'. Reorder the terms: -108t + -2t2 + 30t2 = 108t + -30t2 + -108t + 30t2 Combine like terms: -2t2 + 30t2 = 28t2 -108t + 28t2 = 108t + -30t2 + -108t + 30t2 Reorder the terms: -108t + 28t2 = 108t + -108t + -30t2 + 30t2 Combine like terms: 108t + -108t = 0 -108t + 28t2 = 0 + -30t2 + 30t2 -108t + 28t2 = -30t2 + 30t2 Combine like terms: -30t2 + 30t2 = 0 -108t + 28t2 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(-27 + 7t) = 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 '(-27 + 7t)' equal to zero and attempt to solve: Simplifying -27 + 7t = 0 Solving -27 + 7t = 0 Move all terms containing t to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 7t = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 7t = 0 + 27 7t = 0 + 27 Combine like terms: 0 + 27 = 27 7t = 27 Divide each side by '7'. t = 3.857142857 Simplifying t = 3.857142857Solution
t = {0, 3.857142857}
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