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Simplifying -15t2 + 90t + 105 = 0 Reorder the terms: 105 + 90t + -15t2 = 0 Solving 105 + 90t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(7 + 6t + -1t2) = 0 Factor a trinomial. 15((7 + -1t)(1 + t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Subproblem 2
Set the factor '(1 + t)' equal to zero and attempt to solve: Simplifying 1 + t = 0 Solving 1 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + t = 0 + -1 t = 0 + -1 Combine like terms: 0 + -1 = -1 t = -1 Simplifying t = -1Solution
t = {7, -1}
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