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Simplifying (6t + -9)(4t + -4) = 0 Reorder the terms: (-9 + 6t)(4t + -4) = 0 Reorder the terms: (-9 + 6t)(-4 + 4t) = 0 Multiply (-9 + 6t) * (-4 + 4t) (-9(-4 + 4t) + 6t * (-4 + 4t)) = 0 ((-4 * -9 + 4t * -9) + 6t * (-4 + 4t)) = 0 ((36 + -36t) + 6t * (-4 + 4t)) = 0 (36 + -36t + (-4 * 6t + 4t * 6t)) = 0 (36 + -36t + (-24t + 24t2)) = 0 Combine like terms: -36t + -24t = -60t (36 + -60t + 24t2) = 0 Solving 36 + -60t + 24t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '12'. 12(3 + -5t + 2t2) = 0 Factor a trinomial. 12((1 + -1t)(3 + -2t)) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(3 + -2t)' equal to zero and attempt to solve: Simplifying 3 + -2t = 0 Solving 3 + -2t = 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 + -2t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2t = 0 + -3 -2t = 0 + -3 Combine like terms: 0 + -3 = -3 -2t = -3 Divide each side by '-2'. t = 1.5 Simplifying t = 1.5Solution
t = {1, 1.5}
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