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Simplifying 2T(T + -1) = 24 Reorder the terms: 2T(-1 + T) = 24 (-1 * 2T + T * 2T) = 24 (-2T + 2T2) = 24 Solving -2T + 2T2 = 24 Solving for variable 'T'. Reorder the terms: -24 + -2T + 2T2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -2T + 2T2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -1T + T2) = 0 Factor a trinomial. 2((-3 + -1T)(4 + -1T)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(4 + -1T)' equal to zero and attempt to solve: Simplifying 4 + -1T = 0 Solving 4 + -1T = 0 Move all terms containing T to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1T = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1T = 0 + -4 -1T = 0 + -4 Combine like terms: 0 + -4 = -4 -1T = -4 Divide each side by '-1'. T = 4 Simplifying T = 4Solution
T = {-3, 4}
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