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Simplifying 128t + -8t2 = 312 Solving 128t + -8t2 = 312 Solving for variable 't'. Reorder the terms: -312 + 128t + -8t2 = 312 + -312 Combine like terms: 312 + -312 = 0 -312 + 128t + -8t2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-39 + 16t + -1t2) = 0 Factor a trinomial. 8((-13 + t)(3 + -1t)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-13 + t)' equal to zero and attempt to solve: Simplifying -13 + t = 0 Solving -13 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + t = 0 + 13 t = 0 + 13 Combine like terms: 0 + 13 = 13 t = 13 Simplifying t = 13Subproblem 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 = {13, 3}
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