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Simplifying (8t + 3)(5t + -15) = 0 Reorder the terms: (3 + 8t)(5t + -15) = 0 Reorder the terms: (3 + 8t)(-15 + 5t) = 0 Multiply (3 + 8t) * (-15 + 5t) (3(-15 + 5t) + 8t * (-15 + 5t)) = 0 ((-15 * 3 + 5t * 3) + 8t * (-15 + 5t)) = 0 ((-45 + 15t) + 8t * (-15 + 5t)) = 0 (-45 + 15t + (-15 * 8t + 5t * 8t)) = 0 (-45 + 15t + (-120t + 40t2)) = 0 Combine like terms: 15t + -120t = -105t (-45 + -105t + 40t2) = 0 Solving -45 + -105t + 40t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-9 + -21t + 8t2) = 0 Factor a trinomial. 5((-3 + -8t)(3 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -8t)' equal to zero and attempt to solve: Simplifying -3 + -8t = 0 Solving -3 + -8t = 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 + -8t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -8t = 0 + 3 -8t = 0 + 3 Combine like terms: 0 + 3 = 3 -8t = 3 Divide each side by '-8'. t = -0.375 Simplifying t = -0.375Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.375, 3}
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