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Simplifying 0 = -16t2 + 12t + 40 Reorder the terms: 0 = 40 + 12t + -16t2 Solving 0 = 40 + 12t + -16t2 Solving for variable 't'. Combine like terms: 0 + -40 = -40 -40 + -12t + 16t2 = 40 + 12t + -16t2 + -40 + -12t + 16t2 Reorder the terms: -40 + -12t + 16t2 = 40 + -40 + 12t + -12t + -16t2 + 16t2 Combine like terms: 40 + -40 = 0 -40 + -12t + 16t2 = 0 + 12t + -12t + -16t2 + 16t2 -40 + -12t + 16t2 = 12t + -12t + -16t2 + 16t2 Combine like terms: 12t + -12t = 0 -40 + -12t + 16t2 = 0 + -16t2 + 16t2 -40 + -12t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -40 + -12t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + -3t + 4t2) = 0 Factor a trinomial. 4((-5 + -4t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -4t)' equal to zero and attempt to solve: Simplifying -5 + -4t = 0 Solving -5 + -4t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -4t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4t = 0 + 5 -4t = 0 + 5 Combine like terms: 0 + 5 = 5 -4t = 5 Divide each side by '-4'. t = -1.25 Simplifying t = -1.25Subproblem 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 = {-1.25, 2}
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