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Simplifying (5t + -2)(6t + 9) = 0 Reorder the terms: (-2 + 5t)(6t + 9) = 0 Reorder the terms: (-2 + 5t)(9 + 6t) = 0 Multiply (-2 + 5t) * (9 + 6t) (-2(9 + 6t) + 5t * (9 + 6t)) = 0 ((9 * -2 + 6t * -2) + 5t * (9 + 6t)) = 0 ((-18 + -12t) + 5t * (9 + 6t)) = 0 (-18 + -12t + (9 * 5t + 6t * 5t)) = 0 (-18 + -12t + (45t + 30t2)) = 0 Combine like terms: -12t + 45t = 33t (-18 + 33t + 30t2) = 0 Solving -18 + 33t + 30t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-6 + 11t + 10t2) = 0 Factor a trinomial. 3((-3 + -2t)(2 + -5t)) = 0 Ignore the factor 3.Subproblem 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 '(2 + -5t)' equal to zero and attempt to solve: Simplifying 2 + -5t = 0 Solving 2 + -5t = 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 + -5t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5t = 0 + -2 -5t = 0 + -2 Combine like terms: 0 + -2 = -2 -5t = -2 Divide each side by '-5'. t = 0.4 Simplifying t = 0.4Solution
t = {-1.5, 0.4}
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