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Simplifying 4t(t + -1) = 288 Reorder the terms: 4t(-1 + t) = 288 (-1 * 4t + t * 4t) = 288 (-4t + 4t2) = 288 Solving -4t + 4t2 = 288 Solving for variable 't'. Reorder the terms: -288 + -4t + 4t2 = 288 + -288 Combine like terms: 288 + -288 = 0 -288 + -4t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-72 + -1t + t2) = 0 Factor a trinomial. 4((-8 + -1t)(9 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-8 + -1t)' equal to zero and attempt to solve: Simplifying -8 + -1t = 0 Solving -8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1t = 0 + 8 -1t = 0 + 8 Combine like terms: 0 + 8 = 8 -1t = 8 Divide each side by '-1'. t = -8 Simplifying t = -8Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-8, 9}
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