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Simplifying (6t3) + -1(7t2) + -1(20t) = 0 Remove parenthesis around (7t2) (6t3) + -1 * 7t2 + -1(20t) = 0 Multiply -1 * 7 (6t3) + -7t2 + -1(20t) = 0 Remove parenthesis around (20t) (6t3) + -7t2 + -1 * 20t = 0 Multiply -1 * 20 (6t3) + -7t2 + -20t = 0 Reorder the terms: -20t + -7t2 + (6t3) = 0 Solving -20t + -7t2 + (6t3) = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), 't'. t(-20 + -7t + (6t2)) = 0 Factor a trinomial. t((-4 + -3t)(5 + -2t)) = 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 '(-4 + -3t)' equal to zero and attempt to solve: Simplifying -4 + -3t = 0 Solving -4 + -3t = 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 + -3t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3t = 0 + 4 -3t = 0 + 4 Combine like terms: 0 + 4 = 4 -3t = 4 Divide each side by '-3'. t = -1.333333333 Simplifying t = -1.333333333Subproblem 3
Set the factor '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {0, -1.333333333, 2.5}
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