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Simplifying 272(T) = -16T2 + 96T + 192 Reorder the terms: 272T = 192 + 96T + -16T2 Solving 272T = 192 + 96T + -16T2 Solving for variable 'T'. Reorder the terms: -192 + 272T + -96T + 16T2 = 192 + 96T + -16T2 + -192 + -96T + 16T2 Combine like terms: 272T + -96T = 176T -192 + 176T + 16T2 = 192 + 96T + -16T2 + -192 + -96T + 16T2 Reorder the terms: -192 + 176T + 16T2 = 192 + -192 + 96T + -96T + -16T2 + 16T2 Combine like terms: 192 + -192 = 0 -192 + 176T + 16T2 = 0 + 96T + -96T + -16T2 + 16T2 -192 + 176T + 16T2 = 96T + -96T + -16T2 + 16T2 Combine like terms: 96T + -96T = 0 -192 + 176T + 16T2 = 0 + -16T2 + 16T2 -192 + 176T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 -192 + 176T + 16T2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-12 + 11T + T2) = 0 Factor a trinomial. 16((-12 + -1T)(1 + -1T)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-12 + -1T)' equal to zero and attempt to solve: Simplifying -12 + -1T = 0 Solving -12 + -1T = 0 Move all terms containing T to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1T = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1T = 0 + 12 -1T = 0 + 12 Combine like terms: 0 + 12 = 12 -1T = 12 Divide each side by '-1'. T = -12 Simplifying T = -12Subproblem 2
Set the factor '(1 + -1T)' equal to zero and attempt to solve: Simplifying 1 + -1T = 0 Solving 1 + -1T = 0 Move all terms containing T to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1T = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1T = 0 + -1 -1T = 0 + -1 Combine like terms: 0 + -1 = -1 -1T = -1 Divide each side by '-1'. T = 1 Simplifying T = 1Solution
T = {-12, 1}
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