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Simplifying 105 = -5t2 + -10t + 180 Reorder the terms: 105 = 180 + -10t + -5t2 Solving 105 = 180 + -10t + -5t2 Solving for variable 't'. Combine like terms: 105 + -180 = -75 -75 + 10t + 5t2 = 180 + -10t + -5t2 + -180 + 10t + 5t2 Reorder the terms: -75 + 10t + 5t2 = 180 + -180 + -10t + 10t + -5t2 + 5t2 Combine like terms: 180 + -180 = 0 -75 + 10t + 5t2 = 0 + -10t + 10t + -5t2 + 5t2 -75 + 10t + 5t2 = -10t + 10t + -5t2 + 5t2 Combine like terms: -10t + 10t = 0 -75 + 10t + 5t2 = 0 + -5t2 + 5t2 -75 + 10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -75 + 10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + 2t + t2) = 0 Factor a trinomial. 5((-5 + -1t)(3 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 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 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 2
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 = {-5, 3}
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