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Simplifying 16t2 + 4t + -30 = 0 Reorder the terms: -30 + 4t + 16t2 = 0 Solving -30 + 4t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-15 + 2t + 8t2) = 0 Factor a trinomial. 2((-3 + -2t)(5 + -4t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2t)' equal to zero and attempt to solve: Simplifying -3 + -2t = 0 Solving -3 + -2t = 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 + -2t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2t = 0 + 3 -2t = 0 + 3 Combine like terms: 0 + 3 = 3 -2t = 3 Divide each side by '-2'. t = -1.5 Simplifying t = -1.5Subproblem 2
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 = 1.25Solution
t = {-1.5, 1.25}
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