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Simplifying -15t2 + 120t + 10 = 190 Reorder the terms: 10 + 120t + -15t2 = 190 Solving 10 + 120t + -15t2 = 190 Solving for variable 't'. Reorder the terms: 10 + -190 + 120t + -15t2 = 190 + -190 Combine like terms: 10 + -190 = -180 -180 + 120t + -15t2 = 190 + -190 Combine like terms: 190 + -190 = 0 -180 + 120t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-12 + 8t + -1t2) = 0 Factor a trinomial. 15((-6 + t)(2 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve: Simplifying -6 + t = 0 Solving -6 + t = 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 + t = 0 + 6 Combine like terms: -6 + 6 = 0 0 + t = 0 + 6 t = 0 + 6 Combine like terms: 0 + 6 = 6 t = 6 Simplifying t = 6Subproblem 2
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 = 2Solution
t = {6, 2}
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