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Simplifying (2t + 3)(2t + 3) + -1(t + -2)(t + -2) = 0 Reorder the terms: (3 + 2t)(2t + 3) + -1(t + -2)(t + -2) = 0 Reorder the terms: (3 + 2t)(3 + 2t) + -1(t + -2)(t + -2) = 0 Multiply (3 + 2t) * (3 + 2t) (3(3 + 2t) + 2t * (3 + 2t)) + -1(t + -2)(t + -2) = 0 ((3 * 3 + 2t * 3) + 2t * (3 + 2t)) + -1(t + -2)(t + -2) = 0 ((9 + 6t) + 2t * (3 + 2t)) + -1(t + -2)(t + -2) = 0 (9 + 6t + (3 * 2t + 2t * 2t)) + -1(t + -2)(t + -2) = 0 (9 + 6t + (6t + 4t2)) + -1(t + -2)(t + -2) = 0 Combine like terms: 6t + 6t = 12t (9 + 12t + 4t2) + -1(t + -2)(t + -2) = 0 Reorder the terms: 9 + 12t + 4t2 + -1(-2 + t)(t + -2) = 0 Reorder the terms: 9 + 12t + 4t2 + -1(-2 + t)(-2 + t) = 0 Multiply (-2 + t) * (-2 + t) 9 + 12t + 4t2 + -1(-2(-2 + t) + t(-2 + t)) = 0 9 + 12t + 4t2 + -1((-2 * -2 + t * -2) + t(-2 + t)) = 0 9 + 12t + 4t2 + -1((4 + -2t) + t(-2 + t)) = 0 9 + 12t + 4t2 + -1(4 + -2t + (-2 * t + t * t)) = 0 9 + 12t + 4t2 + -1(4 + -2t + (-2t + t2)) = 0 Combine like terms: -2t + -2t = -4t 9 + 12t + 4t2 + -1(4 + -4t + t2) = 0 9 + 12t + 4t2 + (4 * -1 + -4t * -1 + t2 * -1) = 0 9 + 12t + 4t2 + (-4 + 4t + -1t2) = 0 Reorder the terms: 9 + -4 + 12t + 4t + 4t2 + -1t2 = 0 Combine like terms: 9 + -4 = 5 5 + 12t + 4t + 4t2 + -1t2 = 0 Combine like terms: 12t + 4t = 16t 5 + 16t + 4t2 + -1t2 = 0 Combine like terms: 4t2 + -1t2 = 3t2 5 + 16t + 3t2 = 0 Solving 5 + 16t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (5 + t)(1 + 3t) = 0Subproblem 1
Set the factor '(5 + t)' equal to zero and attempt to solve: Simplifying 5 + t = 0 Solving 5 + t = 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 + t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + t = 0 + -5 t = 0 + -5 Combine like terms: 0 + -5 = -5 t = -5 Simplifying t = -5Subproblem 2
Set the factor '(1 + 3t)' equal to zero and attempt to solve: Simplifying 1 + 3t = 0 Solving 1 + 3t = 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 + 3t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3t = 0 + -1 3t = 0 + -1 Combine like terms: 0 + -1 = -1 3t = -1 Divide each side by '3'. t = -0.3333333333 Simplifying t = -0.3333333333Solution
t = {-5, -0.3333333333}
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