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Simplifying 9t10 + -9t9 + -270t8 = 0 Reorder the terms: -270t8 + -9t9 + 9t10 = 0 Solving -270t8 + -9t9 + 9t10 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '9t8'. 9t8(-30 + -1t + t2) = 0 Factor a trinomial. 9t8((-5 + -1t)(6 + -1t)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 't8' equal to zero and attempt to solve: Simplifying t8 = 0 Solving t8 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t8 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 3
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 = {-5, 6}
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