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Simplifying 315 = 120t + -5t2 Solving 315 = 120t + -5t2 Solving for variable 't'. Reorder the terms: 315 + -120t + 5t2 = 120t + -120t + -5t2 + 5t2 Combine like terms: 120t + -120t = 0 315 + -120t + 5t2 = 0 + -5t2 + 5t2 315 + -120t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 315 + -120t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(63 + -24t + t2) = 0 Factor a trinomial. 5((3 + -1t)(21 + -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 '(21 + -1t)' equal to zero and attempt to solve: Simplifying 21 + -1t = 0 Solving 21 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + -1t = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -1t = 0 + -21 -1t = 0 + -21 Combine like terms: 0 + -21 = -21 -1t = -21 Divide each side by '-1'. t = 21 Simplifying t = 21Solution
t = {3, 21}
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