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Simplifying -16t2 + 76t + 5 = 12t + 5 Reorder the terms: 5 + 76t + -16t2 = 12t + 5 Reorder the terms: 5 + 76t + -16t2 = 5 + 12t Add '-5' to each side of the equation. 5 + 76t + -5 + -16t2 = 5 + -5 + 12t Reorder the terms: 5 + -5 + 76t + -16t2 = 5 + -5 + 12t Combine like terms: 5 + -5 = 0 0 + 76t + -16t2 = 5 + -5 + 12t 76t + -16t2 = 5 + -5 + 12t Combine like terms: 5 + -5 = 0 76t + -16t2 = 0 + 12t 76t + -16t2 = 12t Solving 76t + -16t2 = 12t Solving for variable 't'. Reorder the terms: 76t + -12t + -16t2 = 12t + -12t Combine like terms: 76t + -12t = 64t 64t + -16t2 = 12t + -12t Combine like terms: 12t + -12t = 0 64t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(4 + -1t) = 0 Ignore the factor 16.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {0, 4}
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