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Simplifying t(12t + 5) = 7 Reorder the terms: t(5 + 12t) = 7 (5 * t + 12t * t) = 7 (5t + 12t2) = 7 Solving 5t + 12t2 = 7 Solving for variable 't'. Reorder the terms: -7 + 5t + 12t2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 5t + 12t2 = 0 Factor a trinomial. (-1 + -1t)(7 + -12t) = 0Subproblem 1
Set the factor '(-1 + -1t)' equal to zero and attempt to solve: Simplifying -1 + -1t = 0 Solving -1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1t = 0 + 1 -1t = 0 + 1 Combine like terms: 0 + 1 = 1 -1t = 1 Divide each side by '-1'. t = -1 Simplifying t = -1Subproblem 2
Set the factor '(7 + -12t)' equal to zero and attempt to solve: Simplifying 7 + -12t = 0 Solving 7 + -12t = 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 + -12t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -12t = 0 + -7 -12t = 0 + -7 Combine like terms: 0 + -7 = -7 -12t = -7 Divide each side by '-12'. t = 0.5833333333 Simplifying t = 0.5833333333Solution
t = {-1, 0.5833333333}
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