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Simplifying (2t + 3)(9t + -7) = 0 Reorder the terms: (3 + 2t)(9t + -7) = 0 Reorder the terms: (3 + 2t)(-7 + 9t) = 0 Multiply (3 + 2t) * (-7 + 9t) (3(-7 + 9t) + 2t * (-7 + 9t)) = 0 ((-7 * 3 + 9t * 3) + 2t * (-7 + 9t)) = 0 ((-21 + 27t) + 2t * (-7 + 9t)) = 0 (-21 + 27t + (-7 * 2t + 9t * 2t)) = 0 (-21 + 27t + (-14t + 18t2)) = 0 Combine like terms: 27t + -14t = 13t (-21 + 13t + 18t2) = 0 Solving -21 + 13t + 18t2 = 0 Solving for variable 't'. Factor a trinomial. (-3 + -2t)(7 + -9t) = 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 '(7 + -9t)' equal to zero and attempt to solve: Simplifying 7 + -9t = 0 Solving 7 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -9t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -9t = 0 + -7 -9t = 0 + -7 Combine like terms: 0 + -7 = -7 -9t = -7 Divide each side by '-9'. t = 0.7777777778 Simplifying t = 0.7777777778Solution
t = {-1.5, 0.7777777778}
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