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Simplifying 324 = -16t2 + 12t + 432 Reorder the terms: 324 = 432 + 12t + -16t2 Solving 324 = 432 + 12t + -16t2 Solving for variable 't'. Combine like terms: 324 + -432 = -108 -108 + -12t + 16t2 = 432 + 12t + -16t2 + -432 + -12t + 16t2 Reorder the terms: -108 + -12t + 16t2 = 432 + -432 + 12t + -12t + -16t2 + 16t2 Combine like terms: 432 + -432 = 0 -108 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -108 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -108 + -12t + 16t2 = 0 + -16t2 + 16t2 -108 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -108 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -3t + 4t2) = 0 Factor a trinomial. 4((-9 + -4t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -4t)' equal to zero and attempt to solve: Simplifying -9 + -4t = 0 Solving -9 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4t = 0 + 9 -4t = 0 + 9 Combine like terms: 0 + 9 = 9 -4t = 9 Divide each side by '-4'. t = -2.25 Simplifying t = -2.25Subproblem 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 = {-2.25, 3}
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