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Simplifying (2t + 1)(t + 3) = 0 Reorder the terms: (1 + 2t)(t + 3) = 0 Reorder the terms: (1 + 2t)(3 + t) = 0 Multiply (1 + 2t) * (3 + t) (1(3 + t) + 2t * (3 + t)) = 0 ((3 * 1 + t * 1) + 2t * (3 + t)) = 0 ((3 + 1t) + 2t * (3 + t)) = 0 (3 + 1t + (3 * 2t + t * 2t)) = 0 (3 + 1t + (6t + 2t2)) = 0 Combine like terms: 1t + 6t = 7t (3 + 7t + 2t2) = 0 Solving 3 + 7t + 2t2 = 0 Solving for variable 't'. Factor a trinomial. (3 + t)(1 + 2t) = 0Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Subproblem 2
Set the factor '(1 + 2t)' equal to zero and attempt to solve: Simplifying 1 + 2t = 0 Solving 1 + 2t = 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 + 2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2t = 0 + -1 2t = 0 + -1 Combine like terms: 0 + -1 = -1 2t = -1 Divide each side by '2'. t = -0.5 Simplifying t = -0.5Solution
t = {-3, -0.5}
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