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Simplifying (3d + 6)(5k + 2) = 0 Reorder the terms: (6 + 3d)(5k + 2) = 0 Reorder the terms: (6 + 3d)(2 + 5k) = 0 Multiply (6 + 3d) * (2 + 5k) (6(2 + 5k) + 3d * (2 + 5k)) = 0 ((2 * 6 + 5k * 6) + 3d * (2 + 5k)) = 0 ((12 + 30k) + 3d * (2 + 5k)) = 0 (12 + 30k + (2 * 3d + 5k * 3d)) = 0 (12 + 30k + (6d + 15dk)) = 0 Reorder the terms: (12 + 6d + 15dk + 30k) = 0 (12 + 6d + 15dk + 30k) = 0 Solving 12 + 6d + 15dk + 30k = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 6d + 15dk + -12 + 30k = 0 + -12 Reorder the terms: 12 + -12 + 6d + 15dk + 30k = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 6d + 15dk + 30k = 0 + -12 6d + 15dk + 30k = 0 + -12 Combine like terms: 0 + -12 = -12 6d + 15dk + 30k = -12 Add '-30k' to each side of the equation. 6d + 15dk + 30k + -30k = -12 + -30k Combine like terms: 30k + -30k = 0 6d + 15dk + 0 = -12 + -30k 6d + 15dk = -12 + -30k Reorder the terms: 12 + 6d + 15dk + 30k = -12 + -30k + 12 + 30k Reorder the terms: 12 + 6d + 15dk + 30k = -12 + 12 + -30k + 30k Combine like terms: -12 + 12 = 0 12 + 6d + 15dk + 30k = 0 + -30k + 30k 12 + 6d + 15dk + 30k = -30k + 30k Combine like terms: -30k + 30k = 0 12 + 6d + 15dk + 30k = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 2d + 5dk + 10k) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 2d + 5dk + 10k)' equal to zero and attempt to solve: Simplifying 4 + 2d + 5dk + 10k = 0 Solving 4 + 2d + 5dk + 10k = 0 Move all terms containing d to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 2d + 5dk + -4 + 10k = 0 + -4 Reorder the terms: 4 + -4 + 2d + 5dk + 10k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2d + 5dk + 10k = 0 + -4 2d + 5dk + 10k = 0 + -4 Combine like terms: 0 + -4 = -4 2d + 5dk + 10k = -4 Add '-10k' to each side of the equation. 2d + 5dk + 10k + -10k = -4 + -10k Combine like terms: 10k + -10k = 0 2d + 5dk + 0 = -4 + -10k 2d + 5dk = -4 + -10k The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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