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Simplifying (t + -7)(t + -12) = 0 Reorder the terms: (-7 + t)(t + -12) = 0 Reorder the terms: (-7 + t)(-12 + t) = 0 Multiply (-7 + t) * (-12 + t) (-7(-12 + t) + t(-12 + t)) = 0 ((-12 * -7 + t * -7) + t(-12 + t)) = 0 ((84 + -7t) + t(-12 + t)) = 0 (84 + -7t + (-12 * t + t * t)) = 0 (84 + -7t + (-12t + t2)) = 0 Combine like terms: -7t + -12t = -19t (84 + -19t + t2) = 0 Solving 84 + -19t + t2 = 0 Solving for variable 't'. Factor a trinomial. (7 + -1t)(12 + -1t) = 0Subproblem 1
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 = 7Subproblem 2
Set the factor '(12 + -1t)' equal to zero and attempt to solve: Simplifying 12 + -1t = 0 Solving 12 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1t = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1t = 0 + -12 -1t = 0 + -12 Combine like terms: 0 + -12 = -12 -1t = -12 Divide each side by '-1'. t = 12 Simplifying t = 12Solution
t = {7, 12}
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