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Simplifying 96 = -32t2 + 128t Reorder the terms: 96 = 128t + -32t2 Solving 96 = 128t + -32t2 Solving for variable 't'. Reorder the terms: 96 + -128t + 32t2 = 128t + -128t + -32t2 + 32t2 Combine like terms: 128t + -128t = 0 96 + -128t + 32t2 = 0 + -32t2 + 32t2 96 + -128t + 32t2 = -32t2 + 32t2 Combine like terms: -32t2 + 32t2 = 0 96 + -128t + 32t2 = 0 Factor out the Greatest Common Factor (GCF), '32'. 32(3 + -4t + t2) = 0 Factor a trinomial. 32((1 + -1t)(3 + -1t)) = 0 Ignore the factor 32.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {1, 3}
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