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Simplifying (4t + 9)(t + 8) = 0 Reorder the terms: (9 + 4t)(t + 8) = 0 Reorder the terms: (9 + 4t)(8 + t) = 0 Multiply (9 + 4t) * (8 + t) (9(8 + t) + 4t * (8 + t)) = 0 ((8 * 9 + t * 9) + 4t * (8 + t)) = 0 ((72 + 9t) + 4t * (8 + t)) = 0 (72 + 9t + (8 * 4t + t * 4t)) = 0 (72 + 9t + (32t + 4t2)) = 0 Combine like terms: 9t + 32t = 41t (72 + 41t + 4t2) = 0 Solving 72 + 41t + 4t2 = 0 Solving for variable 't'. Factor a trinomial. (8 + t)(9 + 4t) = 0Subproblem 1
Set the factor '(8 + t)' equal to zero and attempt to solve: Simplifying 8 + t = 0 Solving 8 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + t = 0 + -8 t = 0 + -8 Combine like terms: 0 + -8 = -8 t = -8 Simplifying t = -8Subproblem 2
Set the factor '(9 + 4t)' equal to zero and attempt to solve: Simplifying 9 + 4t = 0 Solving 9 + 4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4t = 0 + -9 4t = 0 + -9 Combine like terms: 0 + -9 = -9 4t = -9 Divide each side by '4'. t = -2.25 Simplifying t = -2.25Solution
t = {-8, -2.25}
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