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Simplifying (t + 5)(t + -9) = 0 Reorder the terms: (5 + t)(t + -9) = 0 Reorder the terms: (5 + t)(-9 + t) = 0 Multiply (5 + t) * (-9 + t) (5(-9 + t) + t(-9 + t)) = 0 ((-9 * 5 + t * 5) + t(-9 + t)) = 0 ((-45 + 5t) + t(-9 + t)) = 0 (-45 + 5t + (-9 * t + t * t)) = 0 (-45 + 5t + (-9t + t2)) = 0 Combine like terms: 5t + -9t = -4t (-45 + -4t + t2) = 0 Solving -45 + -4t + t2 = 0 Solving for variable 't'. Factor a trinomial. (-5 + -1t)(9 + -1t) = 0Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 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 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {-5, 9}
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