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Simplifying (9 + -1t)(3t + -12) = 0 Reorder the terms: (9 + -1t)(-12 + 3t) = 0 Multiply (9 + -1t) * (-12 + 3t) (9(-12 + 3t) + -1t * (-12 + 3t)) = 0 ((-12 * 9 + 3t * 9) + -1t * (-12 + 3t)) = 0 ((-108 + 27t) + -1t * (-12 + 3t)) = 0 (-108 + 27t + (-12 * -1t + 3t * -1t)) = 0 (-108 + 27t + (12t + -3t2)) = 0 Combine like terms: 27t + 12t = 39t (-108 + 39t + -3t2) = 0 Solving -108 + 39t + -3t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-36 + 13t + -1t2) = 0 Factor a trinomial. 3((-9 + t)(4 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + t)' equal to zero and attempt to solve: Simplifying -9 + t = 0 Solving -9 + t = 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 + t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + t = 0 + 9 t = 0 + 9 Combine like terms: 0 + 9 = 9 t = 9 Simplifying t = 9Subproblem 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 = {9, 4}
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