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Simplifying 0 = -4t2 + 17t + 15 Reorder the terms: 0 = 15 + 17t + -4t2 Solving 0 = 15 + 17t + -4t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -17t + 4t2 = 15 + 17t + -4t2 + -15 + -17t + 4t2 Reorder the terms: -15 + -17t + 4t2 = 15 + -15 + 17t + -17t + -4t2 + 4t2 Combine like terms: 15 + -15 = 0 -15 + -17t + 4t2 = 0 + 17t + -17t + -4t2 + 4t2 -15 + -17t + 4t2 = 17t + -17t + -4t2 + 4t2 Combine like terms: 17t + -17t = 0 -15 + -17t + 4t2 = 0 + -4t2 + 4t2 -15 + -17t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -15 + -17t + 4t2 = 0 Factor a trinomial. (-3 + -4t)(5 + -1t) = 0Subproblem 1
Set the factor '(-3 + -4t)' equal to zero and attempt to solve: Simplifying -3 + -4t = 0 Solving -3 + -4t = 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 + -4t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4t = 0 + 3 -4t = 0 + 3 Combine like terms: 0 + 3 = 3 -4t = 3 Divide each side by '-4'. t = -0.75 Simplifying t = -0.75Subproblem 2
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 = 5Solution
t = {-0.75, 5}
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