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Simplifying (7t + 3)(4t + -12) = 0 Reorder the terms: (3 + 7t)(4t + -12) = 0 Reorder the terms: (3 + 7t)(-12 + 4t) = 0 Multiply (3 + 7t) * (-12 + 4t) (3(-12 + 4t) + 7t * (-12 + 4t)) = 0 ((-12 * 3 + 4t * 3) + 7t * (-12 + 4t)) = 0 ((-36 + 12t) + 7t * (-12 + 4t)) = 0 (-36 + 12t + (-12 * 7t + 4t * 7t)) = 0 (-36 + 12t + (-84t + 28t2)) = 0 Combine like terms: 12t + -84t = -72t (-36 + -72t + 28t2) = 0 Solving -36 + -72t + 28t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-9 + -18t + 7t2) = 0 Factor a trinomial. 4((-3 + -7t)(3 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-3 + -7t)' equal to zero and attempt to solve: Simplifying -3 + -7t = 0 Solving -3 + -7t = 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 + -7t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -7t = 0 + 3 -7t = 0 + 3 Combine like terms: 0 + 3 = 3 -7t = 3 Divide each side by '-7'. t = -0.4285714286 Simplifying t = -0.4285714286Subproblem 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 = {-0.4285714286, 3}
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