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Simplifying 32 = -16t2 + 32t + 20 Reorder the terms: 32 = 20 + 32t + -16t2 Solving 32 = 20 + 32t + -16t2 Solving for variable 't'. Combine like terms: 32 + -20 = 12 12 + -32t + 16t2 = 20 + 32t + -16t2 + -20 + -32t + 16t2 Reorder the terms: 12 + -32t + 16t2 = 20 + -20 + 32t + -32t + -16t2 + 16t2 Combine like terms: 20 + -20 = 0 12 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2 12 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 12 + -32t + 16t2 = 0 + -16t2 + 16t2 12 + -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 12 + -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -8t + 4t2) = 0 Factor a trinomial. 4((1 + -2t)(3 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 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 = {0.5, 1.5}
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