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Simplifying 2t2 + 5t = 6t + 15 Reorder the terms: 5t + 2t2 = 6t + 15 Reorder the terms: 5t + 2t2 = 15 + 6t Solving 5t + 2t2 = 15 + 6t Solving for variable 't'. Reorder the terms: -15 + 5t + -6t + 2t2 = 15 + 6t + -15 + -6t Combine like terms: 5t + -6t = -1t -15 + -1t + 2t2 = 15 + 6t + -15 + -6t Reorder the terms: -15 + -1t + 2t2 = 15 + -15 + 6t + -6t Combine like terms: 15 + -15 = 0 -15 + -1t + 2t2 = 0 + 6t + -6t -15 + -1t + 2t2 = 6t + -6t Combine like terms: 6t + -6t = 0 -15 + -1t + 2t2 = 0 Factor a trinomial. (-5 + -2t)(3 + -1t) = 0Subproblem 1
Set the factor '(-5 + -2t)' equal to zero and attempt to solve: Simplifying -5 + -2t = 0 Solving -5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2t = 0 + 5 -2t = 0 + 5 Combine like terms: 0 + 5 = 5 -2t = 5 Divide each side by '-2'. t = -2.5 Simplifying t = -2.5Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve: Simplifying 3 + -1t = 0 Solving 3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1t = 0 + -3 -1t = 0 + -3 Combine like terms: 0 + -3 = -3 -1t = -3 Divide each side by '-1'. t = 3 Simplifying t = 3Solution
t = {-2.5, 3}
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