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Simplifying 24 = 16(t + -1.5)(t + 1) Reorder the terms: 24 = 16(-1.5 + t)(t + 1) Reorder the terms: 24 = 16(-1.5 + t)(1 + t) Multiply (-1.5 + t) * (1 + t) 24 = 16(-1.5(1 + t) + t(1 + t)) 24 = 16((1 * -1.5 + t * -1.5) + t(1 + t)) 24 = 16((-1.5 + -1.5t) + t(1 + t)) 24 = 16(-1.5 + -1.5t + (1 * t + t * t)) 24 = 16(-1.5 + -1.5t + (1t + t2)) Combine like terms: -1.5t + 1t = -0.5t 24 = 16(-1.5 + -0.5t + t2) 24 = (-1.5 * 16 + -0.5t * 16 + t2 * 16) 24 = (-24 + -8t + 16t2) Solving 24 = -24 + -8t + 16t2 Solving for variable 't'. Combine like terms: 24 + 24 = 48 48 + 8t + -16t2 = -24 + -8t + 16t2 + 24 + 8t + -16t2 Reorder the terms: 48 + 8t + -16t2 = -24 + 24 + -8t + 8t + 16t2 + -16t2 Combine like terms: -24 + 24 = 0 48 + 8t + -16t2 = 0 + -8t + 8t + 16t2 + -16t2 48 + 8t + -16t2 = -8t + 8t + 16t2 + -16t2 Combine like terms: -8t + 8t = 0 48 + 8t + -16t2 = 0 + 16t2 + -16t2 48 + 8t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 48 + 8t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(6 + t + -2t2) = 0 Factor a trinomial. 8((2 + -1t)(3 + 2t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(3 + 2t)' equal to zero and attempt to solve: Simplifying 3 + 2t = 0 Solving 3 + 2t = 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 + 2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2t = 0 + -3 2t = 0 + -3 Combine like terms: 0 + -3 = -3 2t = -3 Divide each side by '2'. t = -1.5 Simplifying t = -1.5Solution
t = {2, -1.5}
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