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Simplifying 0 = 16t2 + 80t + 96 Reorder the terms: 0 = 96 + 80t + 16t2 Solving 0 = 96 + 80t + 16t2 Solving for variable 't'. Combine like terms: 0 + -96 = -96 -96 + -80t + -16t2 = 96 + 80t + 16t2 + -96 + -80t + -16t2 Reorder the terms: -96 + -80t + -16t2 = 96 + -96 + 80t + -80t + 16t2 + -16t2 Combine like terms: 96 + -96 = 0 -96 + -80t + -16t2 = 0 + 80t + -80t + 16t2 + -16t2 -96 + -80t + -16t2 = 80t + -80t + 16t2 + -16t2 Combine like terms: 80t + -80t = 0 -96 + -80t + -16t2 = 0 + 16t2 + -16t2 -96 + -80t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 -96 + -80t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '-16'. -16(6 + 5t + t2) = 0 Factor a trinomial. -16((3 + t)(2 + t)) = 0 Ignore the factor -16.Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Subproblem 2
Set the factor '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {-3, -2}
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