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Simplifying 0 = 3t2 + -19t + 20 Reorder the terms: 0 = 20 + -19t + 3t2 Solving 0 = 20 + -19t + 3t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + 19t + -3t2 = 20 + -19t + 3t2 + -20 + 19t + -3t2 Reorder the terms: -20 + 19t + -3t2 = 20 + -20 + -19t + 19t + 3t2 + -3t2 Combine like terms: 20 + -20 = 0 -20 + 19t + -3t2 = 0 + -19t + 19t + 3t2 + -3t2 -20 + 19t + -3t2 = -19t + 19t + 3t2 + -3t2 Combine like terms: -19t + 19t = 0 -20 + 19t + -3t2 = 0 + 3t2 + -3t2 -20 + 19t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -20 + 19t + -3t2 = 0 Factor a trinomial. (-5 + t)(4 + -3t) = 0Subproblem 1
Set the factor '(-5 + t)' equal to zero and attempt to solve: Simplifying -5 + t = 0 Solving -5 + t = 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 + t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + t = 0 + 5 t = 0 + 5 Combine like terms: 0 + 5 = 5 t = 5 Simplifying t = 5Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve: Simplifying 4 + -3t = 0 Solving 4 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3t = 0 + -4 -3t = 0 + -4 Combine like terms: 0 + -4 = -4 -3t = -4 Divide each side by '-3'. t = 1.333333333 Simplifying t = 1.333333333Solution
t = {5, 1.333333333}
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