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Simplifying (4t + 3)(5t + 9) = 0 Reorder the terms: (3 + 4t)(5t + 9) = 0 Reorder the terms: (3 + 4t)(9 + 5t) = 0 Multiply (3 + 4t) * (9 + 5t) (3(9 + 5t) + 4t * (9 + 5t)) = 0 ((9 * 3 + 5t * 3) + 4t * (9 + 5t)) = 0 ((27 + 15t) + 4t * (9 + 5t)) = 0 (27 + 15t + (9 * 4t + 5t * 4t)) = 0 (27 + 15t + (36t + 20t2)) = 0 Combine like terms: 15t + 36t = 51t (27 + 51t + 20t2) = 0 Solving 27 + 51t + 20t2 = 0 Solving for variable 't'. Factor a trinomial. (9 + 5t)(3 + 4t) = 0Subproblem 1
Set the factor '(9 + 5t)' equal to zero and attempt to solve: Simplifying 9 + 5t = 0 Solving 9 + 5t = 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 + 5t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5t = 0 + -9 5t = 0 + -9 Combine like terms: 0 + -9 = -9 5t = -9 Divide each side by '5'. t = -1.8 Simplifying t = -1.8Subproblem 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 = {-1.8, -0.75}
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