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Simplifying (11t + 9)(2t + -6) = 0 Reorder the terms: (9 + 11t)(2t + -6) = 0 Reorder the terms: (9 + 11t)(-6 + 2t) = 0 Multiply (9 + 11t) * (-6 + 2t) (9(-6 + 2t) + 11t * (-6 + 2t)) = 0 ((-6 * 9 + 2t * 9) + 11t * (-6 + 2t)) = 0 ((-54 + 18t) + 11t * (-6 + 2t)) = 0 (-54 + 18t + (-6 * 11t + 2t * 11t)) = 0 (-54 + 18t + (-66t + 22t2)) = 0 Combine like terms: 18t + -66t = -48t (-54 + -48t + 22t2) = 0 Solving -54 + -48t + 22t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -24t + 11t2) = 0 Factor a trinomial. 2((-9 + -11t)(3 + -1t)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -11t)' equal to zero and attempt to solve: Simplifying -9 + -11t = 0 Solving -9 + -11t = 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 + -11t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -11t = 0 + 9 -11t = 0 + 9 Combine like terms: 0 + 9 = 9 -11t = 9 Divide each side by '-11'. t = -0.8181818182 Simplifying t = -0.8181818182Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 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 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-0.8181818182, 3}
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