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Simplifying 12 = -16t2 + 6t + 12 Reorder the terms: 12 = 12 + 6t + -16t2 Add '-12' to each side of the equation. 12 + -12 = 12 + 6t + -12 + -16t2 Combine like terms: 12 + -12 = 0 0 = 12 + 6t + -12 + -16t2 Reorder the terms: 0 = 12 + -12 + 6t + -16t2 Combine like terms: 12 + -12 = 0 0 = 0 + 6t + -16t2 0 = 6t + -16t2 Solving 0 = 6t + -16t2 Solving for variable 't'. Remove the zero: -6t + 16t2 = 6t + -16t2 + -6t + 16t2 Reorder the terms: -6t + 16t2 = 6t + -6t + -16t2 + 16t2 Combine like terms: 6t + -6t = 0 -6t + 16t2 = 0 + -16t2 + 16t2 -6t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -6t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(-3 + 8t) = 0 Ignore the factor 2.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 '(-3 + 8t)' equal to zero and attempt to solve: Simplifying -3 + 8t = 0 Solving -3 + 8t = 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 + 8t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 8t = 0 + 3 8t = 0 + 3 Combine like terms: 0 + 3 = 3 8t = 3 Divide each side by '8'. t = 0.375 Simplifying t = 0.375Solution
t = {0, 0.375}
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