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Simplifying 190 = -15t2 + 105t + 10 Reorder the terms: 190 = 10 + 105t + -15t2 Solving 190 = 10 + 105t + -15t2 Solving for variable 't'. Combine like terms: 190 + -10 = 180 180 + -105t + 15t2 = 10 + 105t + -15t2 + -10 + -105t + 15t2 Reorder the terms: 180 + -105t + 15t2 = 10 + -10 + 105t + -105t + -15t2 + 15t2 Combine like terms: 10 + -10 = 0 180 + -105t + 15t2 = 0 + 105t + -105t + -15t2 + 15t2 180 + -105t + 15t2 = 105t + -105t + -15t2 + 15t2 Combine like terms: 105t + -105t = 0 180 + -105t + 15t2 = 0 + -15t2 + 15t2 180 + -105t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 180 + -105t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(12 + -7t + t2) = 0 Factor a trinomial. 15((3 + -1t)(4 + -1t)) = 0 Ignore the factor 15.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 '(4 + -1t)' equal to zero and attempt to solve: Simplifying 4 + -1t = 0 Solving 4 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1t = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1t = 0 + -4 -1t = 0 + -4 Combine like terms: 0 + -4 = -4 -1t = -4 Divide each side by '-1'. t = 4 Simplifying t = 4Solution
t = {3, 4}
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