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Simplifying 2t(3t + 5) + -4(2 + -4t) = 6(3t + 1) Reorder the terms: 2t(5 + 3t) + -4(2 + -4t) = 6(3t + 1) (5 * 2t + 3t * 2t) + -4(2 + -4t) = 6(3t + 1) (10t + 6t2) + -4(2 + -4t) = 6(3t + 1) 10t + 6t2 + (2 * -4 + -4t * -4) = 6(3t + 1) 10t + 6t2 + (-8 + 16t) = 6(3t + 1) Reorder the terms: -8 + 10t + 16t + 6t2 = 6(3t + 1) Combine like terms: 10t + 16t = 26t -8 + 26t + 6t2 = 6(3t + 1) Reorder the terms: -8 + 26t + 6t2 = 6(1 + 3t) -8 + 26t + 6t2 = (1 * 6 + 3t * 6) -8 + 26t + 6t2 = (6 + 18t) Solving -8 + 26t + 6t2 = 6 + 18t Solving for variable 't'. Reorder the terms: -8 + -6 + 26t + -18t + 6t2 = 6 + 18t + -6 + -18t Combine like terms: -8 + -6 = -14 -14 + 26t + -18t + 6t2 = 6 + 18t + -6 + -18t Combine like terms: 26t + -18t = 8t -14 + 8t + 6t2 = 6 + 18t + -6 + -18t Reorder the terms: -14 + 8t + 6t2 = 6 + -6 + 18t + -18t Combine like terms: 6 + -6 = 0 -14 + 8t + 6t2 = 0 + 18t + -18t -14 + 8t + 6t2 = 18t + -18t Combine like terms: 18t + -18t = 0 -14 + 8t + 6t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 4t + 3t2) = 0 Factor a trinomial. 2((-7 + -3t)(1 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -3t)' equal to zero and attempt to solve: Simplifying -7 + -3t = 0 Solving -7 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -3t = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3t = 0 + 7 -3t = 0 + 7 Combine like terms: 0 + 7 = 7 -3t = 7 Divide each side by '-3'. t = -2.333333333 Simplifying t = -2.333333333Subproblem 2
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 = {-2.333333333, 1}
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