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Simplifying 5t5 + 25t4 + -120t3 = 0 Reorder the terms: -120t3 + 25t4 + 5t5 = 0 Solving -120t3 + 25t4 + 5t5 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5t3'. 5t3(-24 + 5t + t2) = 0 Factor a trinomial. 5t3((-8 + -1t)(3 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 't3' equal to zero and attempt to solve: Simplifying t3 = 0 Solving t3 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t3 = 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 '(-8 + -1t)' equal to zero and attempt to solve: Simplifying -8 + -1t = 0 Solving -8 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -1t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1t = 0 + 8 -1t = 0 + 8 Combine like terms: 0 + 8 = 8 -1t = 8 Divide each side by '-1'. t = -8 Simplifying t = -8Subproblem 3
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 = 3Solution
t = {-8, 3}
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