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Simplifying (4t + 5)(2t + 3) + -12t + -15 = 0 Reorder the terms: (5 + 4t)(2t + 3) + -12t + -15 = 0 Reorder the terms: (5 + 4t)(3 + 2t) + -12t + -15 = 0 Multiply (5 + 4t) * (3 + 2t) (5(3 + 2t) + 4t * (3 + 2t)) + -12t + -15 = 0 ((3 * 5 + 2t * 5) + 4t * (3 + 2t)) + -12t + -15 = 0 ((15 + 10t) + 4t * (3 + 2t)) + -12t + -15 = 0 (15 + 10t + (3 * 4t + 2t * 4t)) + -12t + -15 = 0 (15 + 10t + (12t + 8t2)) + -12t + -15 = 0 Combine like terms: 10t + 12t = 22t (15 + 22t + 8t2) + -12t + -15 = 0 Reorder the terms: 15 + -15 + 22t + -12t + 8t2 = 0 Combine like terms: 15 + -15 = 0 0 + 22t + -12t + 8t2 = 0 22t + -12t + 8t2 = 0 Combine like terms: 22t + -12t = 10t 10t + 8t2 = 0 Solving 10t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(5 + 4t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve: Simplifying 5 + 4t = 0 Solving 5 + 4t = 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 + 4t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4t = 0 + -5 4t = 0 + -5 Combine like terms: 0 + -5 = -5 4t = -5 Divide each side by '4'. t = -1.25 Simplifying t = -1.25Solution
t = {0, -1.25}
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