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Simplifying (2t + -3)(t + 2) = 0 Reorder the terms: (-3 + 2t)(t + 2) = 0 Reorder the terms: (-3 + 2t)(2 + t) = 0 Multiply (-3 + 2t) * (2 + t) (-3(2 + t) + 2t * (2 + t)) = 0 ((2 * -3 + t * -3) + 2t * (2 + t)) = 0 ((-6 + -3t) + 2t * (2 + t)) = 0 (-6 + -3t + (2 * 2t + t * 2t)) = 0 (-6 + -3t + (4t + 2t2)) = 0 Combine like terms: -3t + 4t = 1t (-6 + 1t + 2t2) = 0 Solving -6 + 1t + 2t2 = 0 Solving for variable 't'. Factor a trinomial. (-2 + -1t)(3 + -2t) = 0Subproblem 1
Set the factor '(-2 + -1t)' equal to zero and attempt to solve: Simplifying -2 + -1t = 0 Solving -2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1t = 0 + 2 -1t = 0 + 2 Combine like terms: 0 + 2 = 2 -1t = 2 Divide each side by '-1'. t = -2 Simplifying t = -2Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {-2, 1.5}
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