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Simplifying 0 = 3t2 + -14t + 15 Reorder the terms: 0 = 15 + -14t + 3t2 Solving 0 = 15 + -14t + 3t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + 14t + -3t2 = 15 + -14t + 3t2 + -15 + 14t + -3t2 Reorder the terms: -15 + 14t + -3t2 = 15 + -15 + -14t + 14t + 3t2 + -3t2 Combine like terms: 15 + -15 = 0 -15 + 14t + -3t2 = 0 + -14t + 14t + 3t2 + -3t2 -15 + 14t + -3t2 = -14t + 14t + 3t2 + -3t2 Combine like terms: -14t + 14t = 0 -15 + 14t + -3t2 = 0 + 3t2 + -3t2 -15 + 14t + -3t2 = 3t2 + -3t2 Combine like terms: 3t2 + -3t2 = 0 -15 + 14t + -3t2 = 0 Factor a trinomial. (-3 + t)(5 + -3t) = 0Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Subproblem 2
Set the factor '(5 + -3t)' equal to zero and attempt to solve: Simplifying 5 + -3t = 0 Solving 5 + -3t = 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 + -3t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3t = 0 + -5 -3t = 0 + -5 Combine like terms: 0 + -5 = -5 -3t = -5 Divide each side by '-3'. t = 1.666666667 Simplifying t = 1.666666667Solution
t = {3, 1.666666667}
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