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Simplifying (2d + 3)(3d + -4) = 0 Reorder the terms: (3 + 2d)(3d + -4) = 0 Reorder the terms: (3 + 2d)(-4 + 3d) = 0 Multiply (3 + 2d) * (-4 + 3d) (3(-4 + 3d) + 2d * (-4 + 3d)) = 0 ((-4 * 3 + 3d * 3) + 2d * (-4 + 3d)) = 0 ((-12 + 9d) + 2d * (-4 + 3d)) = 0 (-12 + 9d + (-4 * 2d + 3d * 2d)) = 0 (-12 + 9d + (-8d + 6d2)) = 0 Combine like terms: 9d + -8d = 1d (-12 + 1d + 6d2) = 0 Solving -12 + 1d + 6d2 = 0 Solving for variable 'd'. Factor a trinomial. (-3 + -2d)(4 + -3d) = 0Subproblem 1
Set the factor '(-3 + -2d)' equal to zero and attempt to solve: Simplifying -3 + -2d = 0 Solving -3 + -2d = 0 Move all terms containing d to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -2d = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2d = 0 + 3 -2d = 0 + 3 Combine like terms: 0 + 3 = 3 -2d = 3 Divide each side by '-2'. d = -1.5 Simplifying d = -1.5Subproblem 2
Set the factor '(4 + -3d)' equal to zero and attempt to solve: Simplifying 4 + -3d = 0 Solving 4 + -3d = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3d = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3d = 0 + -4 -3d = 0 + -4 Combine like terms: 0 + -4 = -4 -3d = -4 Divide each side by '-3'. d = 1.333333333 Simplifying d = 1.333333333Solution
d = {-1.5, 1.333333333}
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