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Simplifying t6 + 4t5 + -32t4 = 0 Reorder the terms: -32t4 + 4t5 + t6 = 0 Solving -32t4 + 4t5 + t6 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't4'. t4(-32 + 4t + t2) = 0 Factor a trinomial. t4((-8 + -1t)(4 + -1t)) = 0Subproblem 1
Set the factor 't4' equal to zero and attempt to solve: Simplifying t4 = 0 Solving t4 = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t4 = 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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {-8, 4}
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