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Simplifying 180 = -16t2 + 28t + 240 Reorder the terms: 180 = 240 + 28t + -16t2 Solving 180 = 240 + 28t + -16t2 Solving for variable 't'. Combine like terms: 180 + -240 = -60 -60 + -28t + 16t2 = 240 + 28t + -16t2 + -240 + -28t + 16t2 Reorder the terms: -60 + -28t + 16t2 = 240 + -240 + 28t + -28t + -16t2 + 16t2 Combine like terms: 240 + -240 = 0 -60 + -28t + 16t2 = 0 + 28t + -28t + -16t2 + 16t2 -60 + -28t + 16t2 = 28t + -28t + -16t2 + 16t2 Combine like terms: 28t + -28t = 0 -60 + -28t + 16t2 = 0 + -16t2 + 16t2 -60 + -28t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -60 + -28t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -7t + 4t2) = 0 Factor a trinomial. 4((-5 + -4t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
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 = -1.25Subproblem 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 = {-1.25, 3}
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