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Simplifying 5t(t + -2) = 7t Reorder the terms: 5t(-2 + t) = 7t (-2 * 5t + t * 5t) = 7t (-10t + 5t2) = 7t Solving -10t + 5t2 = 7t Solving for variable 't'. Reorder the terms: -10t + -7t + 5t2 = 7t + -7t Combine like terms: -10t + -7t = -17t -17t + 5t2 = 7t + -7t Combine like terms: 7t + -7t = 0 -17t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-17 + 5t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-17 + 5t)' equal to zero and attempt to solve: Simplifying -17 + 5t = 0 Solving -17 + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 5t = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 5t = 0 + 17 5t = 0 + 17 Combine like terms: 0 + 17 = 17 5t = 17 Divide each side by '5'. t = 3.4 Simplifying t = 3.4Solution
t = {0, 3.4}
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