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Simplifying -16t2 + 300t + -900 = 0 Reorder the terms: -900 + 300t + -16t2 = 0 Solving -900 + 300t + -16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-225 + 75t + -4t2) = 0 Factor a trinomial. 4((-15 + t)(15 + -4t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-15 + t)' equal to zero and attempt to solve: Simplifying -15 + t = 0 Solving -15 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + t = 0 + 15 Combine like terms: -15 + 15 = 0 0 + t = 0 + 15 t = 0 + 15 Combine like terms: 0 + 15 = 15 t = 15 Simplifying t = 15Subproblem 2
Set the factor '(15 + -4t)' equal to zero and attempt to solve: Simplifying 15 + -4t = 0 Solving 15 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -4t = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -4t = 0 + -15 -4t = 0 + -15 Combine like terms: 0 + -15 = -15 -4t = -15 Divide each side by '-4'. t = 3.75 Simplifying t = 3.75Solution
t = {15, 3.75}
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