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Simplifying 0 = 4t3 + -12t2 + -160t Reorder the terms: 0 = -160t + -12t2 + 4t3 Solving 0 = -160t + -12t2 + 4t3 Solving for variable 't'. Remove the zero: 160t + 12t2 + -4t3 = -160t + -12t2 + 4t3 + 160t + 12t2 + -4t3 Reorder the terms: 160t + 12t2 + -4t3 = -160t + 160t + -12t2 + 12t2 + 4t3 + -4t3 Combine like terms: -160t + 160t = 0 160t + 12t2 + -4t3 = 0 + -12t2 + 12t2 + 4t3 + -4t3 160t + 12t2 + -4t3 = -12t2 + 12t2 + 4t3 + -4t3 Combine like terms: -12t2 + 12t2 = 0 160t + 12t2 + -4t3 = 0 + 4t3 + -4t3 160t + 12t2 + -4t3 = 4t3 + -4t3 Combine like terms: 4t3 + -4t3 = 0 160t + 12t2 + -4t3 = 0 Factor out the Greatest Common Factor (GCF), '4t'. 4t(40 + 3t + -1t2) = 0 Factor a trinomial. 4t((8 + -1t)(5 + t)) = 0 Ignore the factor 4.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 '(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 '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Solution
t = {0, 8, -5}
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