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Simplifying 0 = 12t2 + -42t + 30 Reorder the terms: 0 = 30 + -42t + 12t2 Solving 0 = 30 + -42t + 12t2 Solving for variable 't'. Combine like terms: 0 + -30 = -30 -30 + 42t + -12t2 = 30 + -42t + 12t2 + -30 + 42t + -12t2 Reorder the terms: -30 + 42t + -12t2 = 30 + -30 + -42t + 42t + 12t2 + -12t2 Combine like terms: 30 + -30 = 0 -30 + 42t + -12t2 = 0 + -42t + 42t + 12t2 + -12t2 -30 + 42t + -12t2 = -42t + 42t + 12t2 + -12t2 Combine like terms: -42t + 42t = 0 -30 + 42t + -12t2 = 0 + 12t2 + -12t2 -30 + 42t + -12t2 = 12t2 + -12t2 Combine like terms: 12t2 + -12t2 = 0 -30 + 42t + -12t2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-5 + 7t + -2t2) = 0 Factor a trinomial. 6((-5 + 2t)(1 + -1t)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-5 + 2t)' equal to zero and attempt to solve: Simplifying -5 + 2t = 0 Solving -5 + 2t = 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 + 2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2t = 0 + 5 2t = 0 + 5 Combine like terms: 0 + 5 = 5 2t = 5 Divide each side by '2'. t = 2.5 Simplifying t = 2.5Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {2.5, 1}
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