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Simplifying 0 = (T + 8)(3t2 + 4t + 5) Reorder the terms: 0 = (8 + T)(3t2 + 4t + 5) Reorder the terms: 0 = (8 + T)(5 + 4t + 3t2) Multiply (8 + T) * (5 + 4t + 3t2) 0 = (8(5 + 4t + 3t2) + T(5 + 4t + 3t2)) 0 = ((5 * 8 + 4t * 8 + 3t2 * 8) + T(5 + 4t + 3t2)) 0 = ((40 + 32t + 24t2) + T(5 + 4t + 3t2)) 0 = (40 + 32t + 24t2 + (5 * T + 4t * T + 3t2 * T)) 0 = (40 + 32t + 24t2 + (5T + 4tT + 3t2T)) Reorder the terms: 0 = (40 + 5T + 32t + 4tT + 24t2 + 3t2T) 0 = (40 + 5T + 32t + 4tT + 24t2 + 3t2T) Solving 0 = 40 + 5T + 32t + 4tT + 24t2 + 3t2T Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '-5T' to each side of the equation. 0 + -5T = 40 + 5T + 32t + 4tT + 24t2 + -5T + 3t2T Remove the zero: -5T = 40 + 5T + 32t + 4tT + 24t2 + -5T + 3t2T Reorder the terms: -5T = 40 + 5T + -5T + 32t + 4tT + 24t2 + 3t2T Combine like terms: 5T + -5T = 0 -5T = 40 + 0 + 32t + 4tT + 24t2 + 3t2T -5T = 40 + 32t + 4tT + 24t2 + 3t2T Add '-4tT' to each side of the equation. -5T + -4tT = 40 + 32t + 4tT + 24t2 + -4tT + 3t2T Reorder the terms: -5T + -4tT = 40 + 32t + 4tT + -4tT + 24t2 + 3t2T Combine like terms: 4tT + -4tT = 0 -5T + -4tT = 40 + 32t + 0 + 24t2 + 3t2T -5T + -4tT = 40 + 32t + 24t2 + 3t2T Add '-3t2T' to each side of the equation. -5T + -4tT + -3t2T = 40 + 32t + 24t2 + 3t2T + -3t2T Combine like terms: 3t2T + -3t2T = 0 -5T + -4tT + -3t2T = 40 + 32t + 24t2 + 0 -5T + -4tT + -3t2T = 40 + 32t + 24t2 Reorder the terms: -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 40 + 32t + 24t2 + -40 + -32t + -24t2 Reorder the terms: -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 40 + -40 + 32t + -32t + 24t2 + -24t2 Combine like terms: 40 + -40 = 0 -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 0 + 32t + -32t + 24t2 + -24t2 -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 32t + -32t + 24t2 + -24t2 Combine like terms: 32t + -32t = 0 -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 0 + 24t2 + -24t2 -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 24t2 + -24t2 Combine like terms: 24t2 + -24t2 = 0 -40 + -5T + -32t + -4tT + -24t2 + -3t2T = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(40 + 5T + 32t + 4tT + 24t2 + 3t2T) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(40 + 5T + 32t + 4tT + 24t2 + 3t2T)' equal to zero and attempt to solve: Simplifying 40 + 5T + 32t + 4tT + 24t2 + 3t2T = 0 Solving 40 + 5T + 32t + 4tT + 24t2 + 3t2T = 0 Move all terms containing T to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + 5T + 32t + 4tT + 24t2 + -40 + 3t2T = 0 + -40 Reorder the terms: 40 + -40 + 5T + 32t + 4tT + 24t2 + 3t2T = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 5T + 32t + 4tT + 24t2 + 3t2T = 0 + -40 5T + 32t + 4tT + 24t2 + 3t2T = 0 + -40 Combine like terms: 0 + -40 = -40 5T + 32t + 4tT + 24t2 + 3t2T = -40 Add '-32t' to each side of the equation. 5T + 32t + 4tT + 24t2 + -32t + 3t2T = -40 + -32t Reorder the terms: 5T + 32t + -32t + 4tT + 24t2 + 3t2T = -40 + -32t Combine like terms: 32t + -32t = 0 5T + 0 + 4tT + 24t2 + 3t2T = -40 + -32t 5T + 4tT + 24t2 + 3t2T = -40 + -32t Add '-24t2' to each side of the equation. 5T + 4tT + 24t2 + -24t2 + 3t2T = -40 + -32t + -24t2 Combine like terms: 24t2 + -24t2 = 0 5T + 4tT + 0 + 3t2T = -40 + -32t + -24t2 5T + 4tT + 3t2T = -40 + -32t + -24t2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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