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Simplifying 60 = -5t2 + 5t + 210 Reorder the terms: 60 = 210 + 5t + -5t2 Solving 60 = 210 + 5t + -5t2 Solving for variable 't'. Combine like terms: 60 + -210 = -150 -150 + -5t + 5t2 = 210 + 5t + -5t2 + -210 + -5t + 5t2 Reorder the terms: -150 + -5t + 5t2 = 210 + -210 + 5t + -5t + -5t2 + 5t2 Combine like terms: 210 + -210 = 0 -150 + -5t + 5t2 = 0 + 5t + -5t + -5t2 + 5t2 -150 + -5t + 5t2 = 5t + -5t + -5t2 + 5t2 Combine like terms: 5t + -5t = 0 -150 + -5t + 5t2 = 0 + -5t2 + 5t2 -150 + -5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -150 + -5t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-30 + -1t + t2) = 0 Factor a trinomial. 5((-5 + -1t)(6 + -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 '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {-5, 6}
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