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Simplifying (t + -5)(t + -7) = 0 Reorder the terms: (-5 + t)(t + -7) = 0 Reorder the terms: (-5 + t)(-7 + t) = 0 Multiply (-5 + t) * (-7 + t) (-5(-7 + t) + t(-7 + t)) = 0 ((-7 * -5 + t * -5) + t(-7 + t)) = 0 ((35 + -5t) + t(-7 + t)) = 0 (35 + -5t + (-7 * t + t * t)) = 0 (35 + -5t + (-7t + t2)) = 0 Combine like terms: -5t + -7t = -12t (35 + -12t + t2) = 0 Solving 35 + -12t + t2 = 0 Solving for variable 't'. Factor a trinomial. (5 + -1t)(7 + -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 '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 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 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {5, 7}
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