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Simplifying 160 = -15t2 + 105t + 10 Reorder the terms: 160 = 10 + 105t + -15t2 Solving 160 = 10 + 105t + -15t2 Solving for variable 't'. Combine like terms: 160 + -10 = 150 150 + -105t + 15t2 = 10 + 105t + -15t2 + -10 + -105t + 15t2 Reorder the terms: 150 + -105t + 15t2 = 10 + -10 + 105t + -105t + -15t2 + 15t2 Combine like terms: 10 + -10 = 0 150 + -105t + 15t2 = 0 + 105t + -105t + -15t2 + 15t2 150 + -105t + 15t2 = 105t + -105t + -15t2 + 15t2 Combine like terms: 105t + -105t = 0 150 + -105t + 15t2 = 0 + -15t2 + 15t2 150 + -105t + 15t2 = -15t2 + 15t2 Combine like terms: -15t2 + 15t2 = 0 150 + -105t + 15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(10 + -7t + t2) = 0 Factor a trinomial. 15((2 + -1t)(5 + -1t)) = 0 Ignore the factor 15.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 '(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 = {2, 5}
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