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Simplifying -2t2 + 12t + 9 = 9 Reorder the terms: 9 + 12t + -2t2 = 9 Add '-9' to each side of the equation. 9 + 12t + -9 + -2t2 = 9 + -9 Reorder the terms: 9 + -9 + 12t + -2t2 = 9 + -9 Combine like terms: 9 + -9 = 0 0 + 12t + -2t2 = 9 + -9 12t + -2t2 = 9 + -9 Combine like terms: 9 + -9 = 0 12t + -2t2 = 0 Solving 12t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(6 + -1t) = 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 '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Solution
t = {0, 6}
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