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Simplifying (d + 12)(4d + 6) = 0 Reorder the terms: (12 + d)(4d + 6) = 0 Reorder the terms: (12 + d)(6 + 4d) = 0 Multiply (12 + d) * (6 + 4d) (12(6 + 4d) + d(6 + 4d)) = 0 ((6 * 12 + 4d * 12) + d(6 + 4d)) = 0 ((72 + 48d) + d(6 + 4d)) = 0 (72 + 48d + (6 * d + 4d * d)) = 0 (72 + 48d + (6d + 4d2)) = 0 Combine like terms: 48d + 6d = 54d (72 + 54d + 4d2) = 0 Solving 72 + 54d + 4d2 = 0 Solving for variable 'd'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 27d + 2d2) = 0 Factor a trinomial. 2((12 + d)(3 + 2d)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + d)' equal to zero and attempt to solve: Simplifying 12 + d = 0 Solving 12 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + d = 0 + -12 Combine like terms: 12 + -12 = 0 0 + d = 0 + -12 d = 0 + -12 Combine like terms: 0 + -12 = -12 d = -12 Simplifying d = -12Subproblem 2
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 = -1.5Solution
d = {-12, -1.5}
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