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Simplifying 0 = -16t(t + -9)(t + 9) Reorder the terms: 0 = -16t(-9 + t)(t + 9) Reorder the terms: 0 = -16t(-9 + t)(9 + t) Multiply (-9 + t) * (9 + t) 0 = -16t(-9(9 + t) + t(9 + t)) 0 = -16t((9 * -9 + t * -9) + t(9 + t)) 0 = -16t((-81 + -9t) + t(9 + t)) 0 = -16t(-81 + -9t + (9 * t + t * t)) 0 = -16t(-81 + -9t + (9t + t2)) Combine like terms: -9t + 9t = 0 0 = -16t(-81 + 0 + t2) 0 = -16t(-81 + t2) 0 = (-81 * -16t + t2 * -16t) 0 = (1296t + -16t3) Solving 0 = 1296t + -16t3 Solving for variable 't'. Remove the zero: -1296t + 16t3 = 1296t + -16t3 + -1296t + 16t3 Reorder the terms: -1296t + 16t3 = 1296t + -1296t + -16t3 + 16t3 Combine like terms: 1296t + -1296t = 0 -1296t + 16t3 = 0 + -16t3 + 16t3 -1296t + 16t3 = -16t3 + 16t3 Combine like terms: -16t3 + 16t3 = 0 -1296t + 16t3 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(-81 + t2) = 0 Factor a difference between two squares. 16t((9 + t)(-9 + t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(9 + t)' equal to zero and attempt to solve: Simplifying 9 + t = 0 Solving 9 + t = 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 + t = 0 + -9 Combine like terms: 9 + -9 = 0 0 + t = 0 + -9 t = 0 + -9 Combine like terms: 0 + -9 = -9 t = -9 Simplifying t = -9Subproblem 3
Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 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 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9Solution
t = {0, -9, 9}
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