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Simplifying 6t2 + 22t + -40 = 0 Reorder the terms: -40 + 22t + 6t2 = 0 Solving -40 + 22t + 6t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 11t + 3t2) = 0 Factor a trinomial. 2((-5 + -1t)(4 + -3t)) = 0 Ignore the factor 2.Subproblem 1
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 = -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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