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Simplifying -5t2 + 20t + 15 = 3t + 3 Reorder the terms: 15 + 20t + -5t2 = 3t + 3 Reorder the terms: 15 + 20t + -5t2 = 3 + 3t Solving 15 + 20t + -5t2 = 3 + 3t Solving for variable 't'. Reorder the terms: 15 + -3 + 20t + -3t + -5t2 = 3 + 3t + -3 + -3t Combine like terms: 15 + -3 = 12 12 + 20t + -3t + -5t2 = 3 + 3t + -3 + -3t Combine like terms: 20t + -3t = 17t 12 + 17t + -5t2 = 3 + 3t + -3 + -3t Reorder the terms: 12 + 17t + -5t2 = 3 + -3 + 3t + -3t Combine like terms: 3 + -3 = 0 12 + 17t + -5t2 = 0 + 3t + -3t 12 + 17t + -5t2 = 3t + -3t Combine like terms: 3t + -3t = 0 12 + 17t + -5t2 = 0 Factor a trinomial. (4 + -1t)(3 + 5t) = 0Subproblem 1
Set the factor '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Subproblem 2
Set the factor '(3 + 5t)' equal to zero and attempt to solve: Simplifying 3 + 5t = 0 Solving 3 + 5t = 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 + 5t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 5t = 0 + -3 5t = 0 + -3 Combine like terms: 0 + -3 = -3 5t = -3 Divide each side by '5'. t = -0.6 Simplifying t = -0.6Solution
t = {4, -0.6}
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