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Simplifying (5t2 + -7t + 4) + (-6t2 + t + 3) = 0 Reorder the terms: (4 + -7t + 5t2) + (-6t2 + t + 3) = 0 Remove parenthesis around (4 + -7t + 5t2) 4 + -7t + 5t2 + (-6t2 + t + 3) = 0 Reorder the terms: 4 + -7t + 5t2 + (3 + t + -6t2) = 0 Remove parenthesis around (3 + t + -6t2) 4 + -7t + 5t2 + 3 + t + -6t2 = 0 Reorder the terms: 4 + 3 + -7t + t + 5t2 + -6t2 = 0 Combine like terms: 4 + 3 = 7 7 + -7t + t + 5t2 + -6t2 = 0 Combine like terms: -7t + t = -6t 7 + -6t + 5t2 + -6t2 = 0 Combine like terms: 5t2 + -6t2 = -1t2 7 + -6t + -1t2 = 0 Solving 7 + -6t + -1t2 = 0 Solving for variable 't'. Factor a trinomial. (1 + -1t)(7 + t) = 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 + t)' equal to zero and attempt to solve: Simplifying 7 + t = 0 Solving 7 + t = 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 + t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + t = 0 + -7 t = 0 + -7 Combine like terms: 0 + -7 = -7 t = -7 Simplifying t = -7Solution
t = {1, -7}
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