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Simplifying -15t2 + 105t + 10 = 190 Reorder the terms: 10 + 105t + -15t2 = 190 Solving 10 + 105t + -15t2 = 190 Solving for variable 't'. Reorder the terms: 10 + -190 + 105t + -15t2 = 190 + -190 Combine like terms: 10 + -190 = -180 -180 + 105t + -15t2 = 190 + -190 Combine like terms: 190 + -190 = 0 -180 + 105t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-12 + 7t + -1t2) = 0 Factor a trinomial. 15((-4 + t)(3 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-4 + t)' equal to zero and attempt to solve: Simplifying -4 + t = 0 Solving -4 + t = 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 + t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + t = 0 + 4 t = 0 + 4 Combine like terms: 0 + 4 = 4 t = 4 Simplifying t = 4Subproblem 2
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 = 3Solution
t = {4, 3}
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