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Simplifying 0 = 5t + t2 + -84 Reorder the terms: 0 = -84 + 5t + t2 Solving 0 = -84 + 5t + t2 Solving for variable 't'. Combine like terms: 0 + 84 = 84 84 + -5t + -1t2 = -84 + 5t + t2 + 84 + -5t + -1t2 Reorder the terms: 84 + -5t + -1t2 = -84 + 84 + 5t + -5t + t2 + -1t2 Combine like terms: -84 + 84 = 0 84 + -5t + -1t2 = 0 + 5t + -5t + t2 + -1t2 84 + -5t + -1t2 = 5t + -5t + t2 + -1t2 Combine like terms: 5t + -5t = 0 84 + -5t + -1t2 = 0 + t2 + -1t2 84 + -5t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 84 + -5t + -1t2 = 0 Factor a trinomial. (7 + -1t)(12 + t) = 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 + 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 = -12Solution
t = {7, -12}
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