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Simplifying 6[t(t) + -2] + -5t + -38 = 0 Multiply t * t 6[t2 + -2] + -5t + -38 = 0 Reorder the terms: 6[-2 + t2] + -5t + -38 = 0 [-2 * 6 + t2 * 6] + -5t + -38 = 0 [-12 + 6t2] + -5t + -38 = 0 Reorder the terms: -12 + -38 + -5t + 6t2 = 0 Combine like terms: -12 + -38 = -50 -50 + -5t + 6t2 = 0 Solving -50 + -5t + 6t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -2t)(10 + -3t) = 0Subproblem 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 '(10 + -3t)' equal to zero and attempt to solve: Simplifying 10 + -3t = 0 Solving 10 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -3t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -3t = 0 + -10 -3t = 0 + -10 Combine like terms: 0 + -10 = -10 -3t = -10 Divide each side by '-3'. t = 3.333333333 Simplifying t = 3.333333333Solution
t = {-2.5, 3.333333333}
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