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Simplifying -15t2 + 75t + -90 = 0 Reorder the terms: -90 + 75t + -15t2 = 0 Solving -90 + 75t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(-6 + 5t + -1t2) = 0 Factor a trinomial. 15((-3 + t)(2 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 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 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Subproblem 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 = {3, 2}
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