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Simplifying 3t2 = 5t + 2 Reorder the terms: 3t2 = 2 + 5t Solving 3t2 = 2 + 5t Solving for variable 't'. Reorder the terms: -2 + -5t + 3t2 = 2 + 5t + -2 + -5t Reorder the terms: -2 + -5t + 3t2 = 2 + -2 + 5t + -5t Combine like terms: 2 + -2 = 0 -2 + -5t + 3t2 = 0 + 5t + -5t -2 + -5t + 3t2 = 5t + -5t Combine like terms: 5t + -5t = 0 -2 + -5t + 3t2 = 0 Factor a trinomial. (-1 + -3t)(2 + -1t) = 0Subproblem 1
Set the factor '(-1 + -3t)' equal to zero and attempt to solve: Simplifying -1 + -3t = 0 Solving -1 + -3t = 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 + -3t = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3t = 0 + 1 -3t = 0 + 1 Combine like terms: 0 + 1 = 1 -3t = 1 Divide each side by '-3'. t = -0.3333333333 Simplifying t = -0.3333333333Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-0.3333333333, 2}
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