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Simplifying 5t2 = 10t + 75 Reorder the terms: 5t2 = 75 + 10t Solving 5t2 = 75 + 10t Solving for variable 't'. Reorder the terms: -75 + -10t + 5t2 = 75 + 10t + -75 + -10t Reorder the terms: -75 + -10t + 5t2 = 75 + -75 + 10t + -10t Combine like terms: 75 + -75 = 0 -75 + -10t + 5t2 = 0 + 10t + -10t -75 + -10t + 5t2 = 10t + -10t Combine like terms: 10t + -10t = 0 -75 + -10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + -2t + t2) = 0 Factor a trinomial. 5((-3 + -1t)(5 + -1t)) = 0 Ignore the factor 5.Subproblem 1
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 = -3Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve: Simplifying 5 + -1t = 0 Solving 5 + -1t = 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 + -1t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1t = 0 + -5 -1t = 0 + -5 Combine like terms: 0 + -5 = -5 -1t = -5 Divide each side by '-1'. t = 5 Simplifying t = 5Solution
t = {-3, 5}
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