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Simplifying 2t(4t + 3) = 9 Reorder the terms: 2t(3 + 4t) = 9 (3 * 2t + 4t * 2t) = 9 (6t + 8t2) = 9 Solving 6t + 8t2 = 9 Solving for variable 't'. Reorder the terms: -9 + 6t + 8t2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 6t + 8t2 = 0 Factor a trinomial. (-3 + -2t)(3 + -4t) = 0Subproblem 1
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 = -1.5Subproblem 2
Set the factor '(3 + -4t)' equal to zero and attempt to solve: Simplifying 3 + -4t = 0 Solving 3 + -4t = 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 + -4t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4t = 0 + -3 -4t = 0 + -3 Combine like terms: 0 + -3 = -3 -4t = -3 Divide each side by '-4'. t = 0.75 Simplifying t = 0.75Solution
t = {-1.5, 0.75}
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