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Simplifying (13t + 9)(4t + -12) = 0 Reorder the terms: (9 + 13t)(4t + -12) = 0 Reorder the terms: (9 + 13t)(-12 + 4t) = 0 Multiply (9 + 13t) * (-12 + 4t) (9(-12 + 4t) + 13t * (-12 + 4t)) = 0 ((-12 * 9 + 4t * 9) + 13t * (-12 + 4t)) = 0 ((-108 + 36t) + 13t * (-12 + 4t)) = 0 (-108 + 36t + (-12 * 13t + 4t * 13t)) = 0 (-108 + 36t + (-156t + 52t2)) = 0 Combine like terms: 36t + -156t = -120t (-108 + -120t + 52t2) = 0 Solving -108 + -120t + 52t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -30t + 13t2) = 0 Factor a trinomial. 4((-9 + -13t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -13t)' equal to zero and attempt to solve: Simplifying -9 + -13t = 0 Solving -9 + -13t = 0 Move all terms containing t to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -13t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -13t = 0 + 9 -13t = 0 + 9 Combine like terms: 0 + 9 = 9 -13t = 9 Divide each side by '-13'. t = -0.6923076923 Simplifying t = -0.6923076923Subproblem 2
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 = 3Solution
t = {-0.6923076923, 3}
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