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Simplifying T(7x + -6)(5x + 6) = 0 Reorder the terms: T(-6 + 7x)(5x + 6) = 0 Reorder the terms: T(-6 + 7x)(6 + 5x) = 0 Multiply (-6 + 7x) * (6 + 5x) T(-6(6 + 5x) + 7x * (6 + 5x)) = 0 T((6 * -6 + 5x * -6) + 7x * (6 + 5x)) = 0 T((-36 + -30x) + 7x * (6 + 5x)) = 0 T(-36 + -30x + (6 * 7x + 5x * 7x)) = 0 T(-36 + -30x + (42x + 35x2)) = 0 Combine like terms: -30x + 42x = 12x T(-36 + 12x + 35x2) = 0 (-36 * T + 12x * T + 35x2 * T) = 0 (-36T + 12xT + 35x2T) = 0 Solving -36T + 12xT + 35x2T = 0 Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'T'. T(-36 + 12x + 35x2) = 0 Factor a trinomial. T((-6 + -5x)(6 + -7x)) = 0Subproblem 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 '(-6 + -5x)' equal to zero and attempt to solve: Simplifying -6 + -5x = 0 Solving -6 + -5x = 0 Move all terms containing T to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -5x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -5x = 0 + 6 -5x = 0 + 6 Combine like terms: 0 + 6 = 6 -5x = 6 Add '5x' to each side of the equation. -5x + 5x = 6 + 5x Combine like terms: -5x + 5x = 0 0 = 6 + 5x Simplifying 0 = 6 + 5x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(6 + -7x)' equal to zero and attempt to solve: Simplifying 6 + -7x = 0 Solving 6 + -7x = 0 Move all terms containing T to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7x = 0 + -6 -7x = 0 + -6 Combine like terms: 0 + -6 = -6 -7x = -6 Add '7x' to each side of the equation. -7x + 7x = -6 + 7x Combine like terms: -7x + 7x = 0 0 = -6 + 7x Simplifying 0 = -6 + 7x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
T = {0}
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