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Simplifying (8d + 4)(8d + -3) = 0 Reorder the terms: (4 + 8d)(8d + -3) = 0 Reorder the terms: (4 + 8d)(-3 + 8d) = 0 Multiply (4 + 8d) * (-3 + 8d) (4(-3 + 8d) + 8d * (-3 + 8d)) = 0 ((-3 * 4 + 8d * 4) + 8d * (-3 + 8d)) = 0 ((-12 + 32d) + 8d * (-3 + 8d)) = 0 (-12 + 32d + (-3 * 8d + 8d * 8d)) = 0 (-12 + 32d + (-24d + 64d2)) = 0 Combine like terms: 32d + -24d = 8d (-12 + 8d + 64d2) = 0 Solving -12 + 8d + 64d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '4'. 4(-3 + 2d + 16d2) = 0 Factor a trinomial. 4((-1 + -2d)(3 + -8d)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -2d)' equal to zero and attempt to solve: Simplifying -1 + -2d = 0 Solving -1 + -2d = 0 Move all terms containing d to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -2d = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2d = 0 + 1 -2d = 0 + 1 Combine like terms: 0 + 1 = 1 -2d = 1 Divide each side by '-2'. d = -0.5 Simplifying d = -0.5Subproblem 2
Set the factor '(3 + -8d)' equal to zero and attempt to solve: Simplifying 3 + -8d = 0 Solving 3 + -8d = 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 + -8d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8d = 0 + -3 -8d = 0 + -3 Combine like terms: 0 + -3 = -3 -8d = -3 Divide each side by '-8'. d = 0.375 Simplifying d = 0.375Solution
d = {-0.5, 0.375}
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