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Simplifying 4t(t2 + 4t + 2) + -2t(3t2 + -6t + 17) = 0 Reorder the terms: 4t(2 + 4t + t2) + -2t(3t2 + -6t + 17) = 0 (2 * 4t + 4t * 4t + t2 * 4t) + -2t(3t2 + -6t + 17) = 0 (8t + 16t2 + 4t3) + -2t(3t2 + -6t + 17) = 0 Reorder the terms: 8t + 16t2 + 4t3 + -2t(17 + -6t + 3t2) = 0 8t + 16t2 + 4t3 + (17 * -2t + -6t * -2t + 3t2 * -2t) = 0 8t + 16t2 + 4t3 + (-34t + 12t2 + -6t3) = 0 Reorder the terms: 8t + -34t + 16t2 + 12t2 + 4t3 + -6t3 = 0 Combine like terms: 8t + -34t = -26t -26t + 16t2 + 12t2 + 4t3 + -6t3 = 0 Combine like terms: 16t2 + 12t2 = 28t2 -26t + 28t2 + 4t3 + -6t3 = 0 Combine like terms: 4t3 + -6t3 = -2t3 -26t + 28t2 + -2t3 = 0 Solving -26t + 28t2 + -2t3 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2t'. 2t(-13 + 14t + -1t2) = 0 Factor a trinomial. 2t((-13 + t)(1 + -1t)) = 0 Ignore the factor 2.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 '(-13 + t)' equal to zero and attempt to solve: Simplifying -13 + t = 0 Solving -13 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + t = 0 + 13 Combine like terms: -13 + 13 = 0 0 + t = 0 + 13 t = 0 + 13 Combine like terms: 0 + 13 = 13 t = 13 Simplifying t = 13Subproblem 3
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {0, 13, 1}
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