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Simplifying 4t(9t + -4)(4t + -1) = 0 Reorder the terms: 4t(-4 + 9t)(4t + -1) = 0 Reorder the terms: 4t(-4 + 9t)(-1 + 4t) = 0 Multiply (-4 + 9t) * (-1 + 4t) 4t(-4(-1 + 4t) + 9t * (-1 + 4t)) = 0 4t((-1 * -4 + 4t * -4) + 9t * (-1 + 4t)) = 0 4t((4 + -16t) + 9t * (-1 + 4t)) = 0 4t(4 + -16t + (-1 * 9t + 4t * 9t)) = 0 4t(4 + -16t + (-9t + 36t2)) = 0 Combine like terms: -16t + -9t = -25t 4t(4 + -25t + 36t2) = 0 (4 * 4t + -25t * 4t + 36t2 * 4t) = 0 (16t + -100t2 + 144t3) = 0 Solving 16t + -100t2 + 144t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4t'. 4t(4 + -25t + 36t2) = 0 Factor a trinomial. 4t((1 + -4t)(4 + -9t)) = 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 '(4 + -9t)' equal to zero and attempt to solve: Simplifying 4 + -9t = 0 Solving 4 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -9t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -9t = 0 + -4 -9t = 0 + -4 Combine like terms: 0 + -4 = -4 -9t = -4 Divide each side by '-9'. t = 0.4444444444 Simplifying t = 0.4444444444Solution
t = {0, 0.25, 0.4444444444}
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