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Simplifying (-5 + 3t)(-5 + -6t) = 0 Multiply (-5 + 3t) * (-5 + -6t) (-5(-5 + -6t) + 3t * (-5 + -6t)) = 0 ((-5 * -5 + -6t * -5) + 3t * (-5 + -6t)) = 0 ((25 + 30t) + 3t * (-5 + -6t)) = 0 (25 + 30t + (-5 * 3t + -6t * 3t)) = 0 (25 + 30t + (-15t + -18t2)) = 0 Combine like terms: 30t + -15t = 15t (25 + 15t + -18t2) = 0 Solving 25 + 15t + -18t2 = 0 Solving for variable 't'. Factor a trinomial. (5 + -3t)(5 + 6t) = 0Subproblem 1
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 = 1.666666667Subproblem 2
Set the factor '(5 + 6t)' equal to zero and attempt to solve: Simplifying 5 + 6t = 0 Solving 5 + 6t = 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 + 6t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6t = 0 + -5 6t = 0 + -5 Combine like terms: 0 + -5 = -5 6t = -5 Divide each side by '6'. t = -0.8333333333 Simplifying t = -0.8333333333Solution
t = {1.666666667, -0.8333333333}
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