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Simplifying 64t3 + -4t = 0 Reorder the terms: -4t + 64t3 = 0 Solving -4t + 64t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(-1 + 16t2) = 0 Factor a difference between two squares. 4t((1 + 4t)(-1 + 4t)) = 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 '(1 + 4t)' equal to zero and attempt to solve: Simplifying 1 + 4t = 0 Solving 1 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4t = 0 + -1 4t = 0 + -1 Combine like terms: 0 + -1 = -1 4t = -1 Divide each side by '4'. t = -0.25 Simplifying t = -0.25Subproblem 3
Set the factor '(-1 + 4t)' equal to zero and attempt to solve: Simplifying -1 + 4t = 0 Solving -1 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 4t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 4t = 0 + 1 4t = 0 + 1 Combine like terms: 0 + 1 = 1 4t = 1 Divide each side by '4'. t = 0.25 Simplifying t = 0.25Solution
t = {0, -0.25, 0.25}
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