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Simplifying 270 = 75t + -5t2 Solving 270 = 75t + -5t2 Solving for variable 't'. Reorder the terms: 270 + -75t + 5t2 = 75t + -75t + -5t2 + 5t2 Combine like terms: 75t + -75t = 0 270 + -75t + 5t2 = 0 + -5t2 + 5t2 270 + -75t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 270 + -75t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(54 + -15t + t2) = 0 Factor a trinomial. 5((6 + -1t)(9 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(6 + -1t)' equal to zero and attempt to solve: Simplifying 6 + -1t = 0 Solving 6 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1t = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1t = 0 + -6 -1t = 0 + -6 Combine like terms: 0 + -6 = -6 -1t = -6 Divide each side by '-1'. t = 6 Simplifying t = 6Subproblem 2
Set the factor '(9 + -1t)' equal to zero and attempt to solve: Simplifying 9 + -1t = 0 Solving 9 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1t = 0 + -9 -1t = 0 + -9 Combine like terms: 0 + -9 = -9 -1t = -9 Divide each side by '-1'. t = 9 Simplifying t = 9Solution
t = {6, 9}
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