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Simplifying (3t + -8) + -1t(8 + -3t) = 0 Reorder the terms: (-8 + 3t) + -1t(8 + -3t) = 0 Remove parenthesis around (-8 + 3t) -8 + 3t + -1t(8 + -3t) = 0 -8 + 3t + (8 * -1t + -3t * -1t) = 0 -8 + 3t + (-8t + 3t2) = 0 Combine like terms: 3t + -8t = -5t -8 + -5t + 3t2 = 0 Solving -8 + -5t + 3t2 = 0 Solving for variable 't'. Factor a trinomial. (-1 + -1t)(8 + -3t) = 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 '(8 + -3t)' equal to zero and attempt to solve: Simplifying 8 + -3t = 0 Solving 8 + -3t = 0 Move all terms containing t to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3t = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3t = 0 + -8 -3t = 0 + -8 Combine like terms: 0 + -8 = -8 -3t = -8 Divide each side by '-3'. t = 2.666666667 Simplifying t = 2.666666667Solution
t = {-1, 2.666666667}
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