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Simplifying 10t3 + -5t2 + -75t = 0 Reorder the terms: -75t + -5t2 + 10t3 = 0 Solving -75t + -5t2 + 10t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5t'. 5t(-15 + -1t + 2t2) = 0 Factor a trinomial. 5t((-5 + -2t)(3 + -1t)) = 0 Ignore the factor 5.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 '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 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 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5Subproblem 3
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 = 3Solution
t = {0, -2.5, 3}
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