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Simplifying 3t(4t + 1)(4t + 1) = 0 Reorder the terms: 3t(1 + 4t)(4t + 1) = 0 Reorder the terms: 3t(1 + 4t)(1 + 4t) = 0 Multiply (1 + 4t) * (1 + 4t) 3t(1(1 + 4t) + 4t * (1 + 4t)) = 0 3t((1 * 1 + 4t * 1) + 4t * (1 + 4t)) = 0 3t((1 + 4t) + 4t * (1 + 4t)) = 0 3t(1 + 4t + (1 * 4t + 4t * 4t)) = 0 3t(1 + 4t + (4t + 16t2)) = 0 Combine like terms: 4t + 4t = 8t 3t(1 + 8t + 16t2) = 0 (1 * 3t + 8t * 3t + 16t2 * 3t) = 0 (3t + 24t2 + 48t3) = 0 Solving 3t + 24t2 + 48t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3t'. 3t(1 + 8t + 16t2) = 0 Factor a trinomial. 3t((1 + 4t)(1 + 4t)) = 0 Ignore the factor 3.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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