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Simplifying 45t2 + -27t + -18 = 0 Reorder the terms: -18 + -27t + 45t2 = 0 Solving -18 + -27t + 45t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '9'. 9(-2 + -3t + 5t2) = 0 Factor a trinomial. 9((-2 + -5t)(1 + -1t)) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-2 + -5t)' equal to zero and attempt to solve: Simplifying -2 + -5t = 0 Solving -2 + -5t = 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 + -5t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5t = 0 + 2 -5t = 0 + 2 Combine like terms: 0 + 2 = 2 -5t = 2 Divide each side by '-5'. t = -0.4 Simplifying t = -0.4Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {-0.4, 1}
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