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Simplifying 4t10 + -28t9 + -120t8 = 0 Reorder the terms: -120t8 + -28t9 + 4t10 = 0 Solving -120t8 + -28t9 + 4t10 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t8'. 4t8(-30 + -7t + t2) = 0 Factor a trinomial. 4t8((-3 + -1t)(10 + -1t)) = 0 Ignore the factor 4.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 '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 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 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 3
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {-3, 10}
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