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Simplifying 20 = -16t2 + 32t + 20 Reorder the terms: 20 = 20 + 32t + -16t2 Add '-20' to each side of the equation. 20 + -20 = 20 + 32t + -20 + -16t2 Combine like terms: 20 + -20 = 0 0 = 20 + 32t + -20 + -16t2 Reorder the terms: 0 = 20 + -20 + 32t + -16t2 Combine like terms: 20 + -20 = 0 0 = 0 + 32t + -16t2 0 = 32t + -16t2 Solving 0 = 32t + -16t2 Solving for variable 't'. Remove the zero: -32t + 16t2 = 32t + -16t2 + -32t + 16t2 Reorder the terms: -32t + 16t2 = 32t + -32t + -16t2 + 16t2 Combine like terms: 32t + -32t = 0 -32t + 16t2 = 0 + -16t2 + 16t2 -32t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -32t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16t'. 16t(-2 + 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 '(-2 + t)' equal to zero and attempt to solve: Simplifying -2 + t = 0 Solving -2 + t = 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 + t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + t = 0 + 2 t = 0 + 2 Combine like terms: 0 + 2 = 2 t = 2 Simplifying t = 2Solution
t = {0, 2}
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