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Simplifying -16t2 + 112t + -180 = 0 Reorder the terms: -180 + 112t + -16t2 = 0 Solving -180 + 112t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-45 + 28t + -4t2) = 0 Factor a trinomial. 4((-9 + 2t)(5 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + 2t)' equal to zero and attempt to solve: Simplifying -9 + 2t = 0 Solving -9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t = 0 + 9 2t = 0 + 9 Combine like terms: 0 + 9 = 9 2t = 9 Divide each side by '2'. t = 4.5 Simplifying t = 4.5Subproblem 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 = 2.5Solution
t = {4.5, 2.5}
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