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Simplifying 5t3 + 60t2 = -180t Reorder the terms: 60t2 + 5t3 = -180t Solving 60t2 + 5t3 = -180t Solving for variable 't'. Reorder the terms: 180t + 60t2 + 5t3 = -180t + 180t Combine like terms: -180t + 180t = 0 180t + 60t2 + 5t3 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(36 + 12t + t2) = 0 Factor a trinomial. 5t((6 + t)(6 + t)) = 0 Ignore the factor 5.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 '(6 + t)' equal to zero and attempt to solve: Simplifying 6 + t = 0 Solving 6 + t = 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 + t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + t = 0 + -6 t = 0 + -6 Combine like terms: 0 + -6 = -6 t = -6 Simplifying t = -6Subproblem 3
Set the factor '(6 + t)' equal to zero and attempt to solve: Simplifying 6 + t = 0 Solving 6 + t = 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 + t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + t = 0 + -6 t = 0 + -6 Combine like terms: 0 + -6 = -6 t = -6 Simplifying t = -6Solution
t = {0, -6, -6}
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