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Simplifying 120 = -6t2 + 6t + 120 Reorder the terms: 120 = 120 + 6t + -6t2 Add '-120' to each side of the equation. 120 + -120 = 120 + 6t + -120 + -6t2 Combine like terms: 120 + -120 = 0 0 = 120 + 6t + -120 + -6t2 Reorder the terms: 0 = 120 + -120 + 6t + -6t2 Combine like terms: 120 + -120 = 0 0 = 0 + 6t + -6t2 0 = 6t + -6t2 Solving 0 = 6t + -6t2 Solving for variable 't'. Remove the zero: -6t + 6t2 = 6t + -6t2 + -6t + 6t2 Reorder the terms: -6t + 6t2 = 6t + -6t + -6t2 + 6t2 Combine like terms: 6t + -6t = 0 -6t + 6t2 = 0 + -6t2 + 6t2 -6t + 6t2 = -6t2 + 6t2 Combine like terms: -6t2 + 6t2 = 0 -6t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '6t'. 6t(-1 + t) = 0 Ignore the factor 6.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 '(-1 + t)' equal to zero and attempt to solve: Simplifying -1 + t = 0 Solving -1 + t = 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 + t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + t = 0 + 1 t = 0 + 1 Combine like terms: 0 + 1 = 1 t = 1 Simplifying t = 1Solution
t = {0, 1}
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