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Simplifying 30 = 5t + 5t * t Multiply t * t 30 = 5t + 5t2 Solving 30 = 5t + 5t2 Solving for variable 't'. Reorder the terms: 30 + -5t + -5t2 = 5t + -5t + 5t2 + -5t2 Combine like terms: 5t + -5t = 0 30 + -5t + -5t2 = 0 + 5t2 + -5t2 30 + -5t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 30 + -5t + -5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(6 + -1t + -1t2) = 0 Factor a trinomial. 5((2 + -1t)(3 + t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Subproblem 2
Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3Solution
t = {2, -3}
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