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Simplifying 4t3 + -81t = 0 Reorder the terms: -81t + 4t3 = 0 Solving -81t + 4t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-81 + 4t2) = 0 Factor a difference between two squares. t((9 + 2t)(-9 + 2t)) = 0Subproblem 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 '(9 + 2t)' equal to zero and attempt to solve: Simplifying 9 + 2t = 0 Solving 9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 2t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2t = 0 + -9 2t = 0 + -9 Combine like terms: 0 + -9 = -9 2t = -9 Divide each side by '2'. t = -4.5 Simplifying t = -4.5Subproblem 3
Set the factor '(-9 + 2t)' equal to zero and attempt to solve: Simplifying -9 + 2t = 0 Solving -9 + 2t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + 2t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 2t = 0 + 9 2t = 0 + 9 Combine like terms: 0 + 9 = 9 2t = 9 Divide each side by '2'. t = 4.5 Simplifying t = 4.5Solution
t = {0, -4.5, 4.5}
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