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Simplifying t(19 + -1t) = 84 (19 * t + -1t * t) = 84 (19t + -1t2) = 84 Solving 19t + -1t2 = 84 Solving for variable 't'. Reorder the terms: -84 + 19t + -1t2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 19t + -1t2 = 0 Factor a trinomial. (-12 + t)(7 + -1t) = 0Subproblem 1
Set the factor '(-12 + t)' equal to zero and attempt to solve: Simplifying -12 + t = 0 Solving -12 + t = 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 + t = 0 + 12 Combine like terms: -12 + 12 = 0 0 + t = 0 + 12 t = 0 + 12 Combine like terms: 0 + 12 = 12 t = 12 Simplifying t = 12Subproblem 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 = {12, 7}
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