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Simplifying 0 = -5t2 + 17t + 12 Reorder the terms: 0 = 12 + 17t + -5t2 Solving 0 = 12 + 17t + -5t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -17t + 5t2 = 12 + 17t + -5t2 + -12 + -17t + 5t2 Reorder the terms: -12 + -17t + 5t2 = 12 + -12 + 17t + -17t + -5t2 + 5t2 Combine like terms: 12 + -12 = 0 -12 + -17t + 5t2 = 0 + 17t + -17t + -5t2 + 5t2 -12 + -17t + 5t2 = 17t + -17t + -5t2 + 5t2 Combine like terms: 17t + -17t = 0 -12 + -17t + 5t2 = 0 + -5t2 + 5t2 -12 + -17t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -12 + -17t + 5t2 = 0 Factor a trinomial. (-3 + -5t)(4 + -1t) = 0Subproblem 1
Set the factor '(-3 + -5t)' equal to zero and attempt to solve: Simplifying -3 + -5t = 0 Solving -3 + -5t = 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 + -5t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5t = 0 + 3 -5t = 0 + 3 Combine like terms: 0 + 3 = 3 -5t = 3 Divide each side by '-5'. t = -0.6 Simplifying t = -0.6Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 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 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-0.6, 4}
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