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Simplifying (9t + 5)(4t + -12) = 0 Reorder the terms: (5 + 9t)(4t + -12) = 0 Reorder the terms: (5 + 9t)(-12 + 4t) = 0 Multiply (5 + 9t) * (-12 + 4t) (5(-12 + 4t) + 9t * (-12 + 4t)) = 0 ((-12 * 5 + 4t * 5) + 9t * (-12 + 4t)) = 0 ((-60 + 20t) + 9t * (-12 + 4t)) = 0 (-60 + 20t + (-12 * 9t + 4t * 9t)) = 0 (-60 + 20t + (-108t + 36t2)) = 0 Combine like terms: 20t + -108t = -88t (-60 + -88t + 36t2) = 0 Solving -60 + -88t + 36t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-15 + -22t + 9t2) = 0 Factor a trinomial. 4((-5 + -9t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -9t)' equal to zero and attempt to solve: Simplifying -5 + -9t = 0 Solving -5 + -9t = 0 Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -9t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -9t = 0 + 5 -9t = 0 + 5 Combine like terms: 0 + 5 = 5 -9t = 5 Divide each side by '-9'. t = -0.5555555556 Simplifying t = -0.5555555556Subproblem 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 = {-0.5555555556, 3}
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