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Simplifying -8t = 4t(t + 5) + 2t Reorder the terms: -8t = 4t(5 + t) + 2t -8t = (5 * 4t + t * 4t) + 2t -8t = (20t + 4t2) + 2t Reorder the terms: -8t = 20t + 2t + 4t2 Combine like terms: 20t + 2t = 22t -8t = 22t + 4t2 Solving -8t = 22t + 4t2 Solving for variable 't'. Combine like terms: -8t + -22t = -30t -30t + -4t2 = 22t + 4t2 + -22t + -4t2 Reorder the terms: -30t + -4t2 = 22t + -22t + 4t2 + -4t2 Combine like terms: 22t + -22t = 0 -30t + -4t2 = 0 + 4t2 + -4t2 -30t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 -30t + -4t2 = 0 Factor out the Greatest Common Factor (GCF), '-2t'. -2t(15 + 2t) = 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 '(15 + 2t)' equal to zero and attempt to solve: Simplifying 15 + 2t = 0 Solving 15 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + 2t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 2t = 0 + -15 2t = 0 + -15 Combine like terms: 0 + -15 = -15 2t = -15 Divide each side by '2'. t = -7.5 Simplifying t = -7.5Solution
t = {0, -7.5}
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