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Simplifying 9t3 + -64t = 0 Reorder the terms: -64t + 9t3 = 0 Solving -64t + 9t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-64 + 9t2) = 0 Factor a difference between two squares. t((8 + 3t)(-8 + 3t)) = 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 '(8 + 3t)' equal to zero and attempt to solve: Simplifying 8 + 3t = 0 Solving 8 + 3t = 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 + 3t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3t = 0 + -8 3t = 0 + -8 Combine like terms: 0 + -8 = -8 3t = -8 Divide each side by '3'. t = -2.666666667 Simplifying t = -2.666666667Subproblem 3
Set the factor '(-8 + 3t)' equal to zero and attempt to solve: Simplifying -8 + 3t = 0 Solving -8 + 3t = 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 + 3t = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3t = 0 + 8 3t = 0 + 8 Combine like terms: 0 + 8 = 8 3t = 8 Divide each side by '3'. t = 2.666666667 Simplifying t = 2.666666667Solution
t = {0, -2.666666667, 2.666666667}
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