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Simplifying (7t + 4)(3t + -9) = 0 Reorder the terms: (4 + 7t)(3t + -9) = 0 Reorder the terms: (4 + 7t)(-9 + 3t) = 0 Multiply (4 + 7t) * (-9 + 3t) (4(-9 + 3t) + 7t * (-9 + 3t)) = 0 ((-9 * 4 + 3t * 4) + 7t * (-9 + 3t)) = 0 ((-36 + 12t) + 7t * (-9 + 3t)) = 0 (-36 + 12t + (-9 * 7t + 3t * 7t)) = 0 (-36 + 12t + (-63t + 21t2)) = 0 Combine like terms: 12t + -63t = -51t (-36 + -51t + 21t2) = 0 Solving -36 + -51t + 21t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -17t + 7t2) = 0 Factor a trinomial. 3((-4 + -7t)(3 + -1t)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + -7t)' equal to zero and attempt to solve: Simplifying -4 + -7t = 0 Solving -4 + -7t = 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 + -7t = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -7t = 0 + 4 -7t = 0 + 4 Combine like terms: 0 + 4 = 4 -7t = 4 Divide each side by '-7'. t = -0.5714285714 Simplifying t = -0.5714285714Subproblem 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 = {-0.5714285714, 3}
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