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Simplifying 2(4dm + -3n + 1) + -6n(2d + -1) + 2(2d + -1) = 0 Reorder the terms: 2(1 + 4dm + -3n) + -6n(2d + -1) + 2(2d + -1) = 0 (1 * 2 + 4dm * 2 + -3n * 2) + -6n(2d + -1) + 2(2d + -1) = 0 (2 + 8dm + -6n) + -6n(2d + -1) + 2(2d + -1) = 0 Reorder the terms: 2 + 8dm + -6n + -6n(-1 + 2d) + 2(2d + -1) = 0 2 + 8dm + -6n + (-1 * -6n + 2d * -6n) + 2(2d + -1) = 0 Reorder the terms: 2 + 8dm + -6n + (-12dn + 6n) + 2(2d + -1) = 0 2 + 8dm + -6n + (-12dn + 6n) + 2(2d + -1) = 0 Reorder the terms: 2 + 8dm + -6n + -12dn + 6n + 2(-1 + 2d) = 0 2 + 8dm + -6n + -12dn + 6n + (-1 * 2 + 2d * 2) = 0 2 + 8dm + -6n + -12dn + 6n + (-2 + 4d) = 0 Reorder the terms: 2 + -2 + 4d + 8dm + -12dn + -6n + 6n = 0 Combine like terms: 2 + -2 = 0 0 + 4d + 8dm + -12dn + -6n + 6n = 0 4d + 8dm + -12dn + -6n + 6n = 0 Combine like terms: -6n + 6n = 0 4d + 8dm + -12dn + 0 = 0 4d + 8dm + -12dn = 0 Solving 4d + 8dm + -12dn = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4d'. 4d(1 + 2m + -3n) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'd' equal to zero and attempt to solve: Simplifying d = 0 Solving d = 0 Move all terms containing d to the left, all other terms to the right. Simplifying d = 0Subproblem 2
Set the factor '(1 + 2m + -3n)' equal to zero and attempt to solve: Simplifying 1 + 2m + -3n = 0 Solving 1 + 2m + -3n = 0 Move all terms containing d to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 2m + -1 + -3n = 0 + -1 Reorder the terms: 1 + -1 + 2m + -3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2m + -3n = 0 + -1 2m + -3n = 0 + -1 Combine like terms: 0 + -1 = -1 2m + -3n = -1 Add '-2m' to each side of the equation. 2m + -2m + -3n = -1 + -2m Combine like terms: 2m + -2m = 0 0 + -3n = -1 + -2m -3n = -1 + -2m Add '3n' to each side of the equation. -3n + 3n = -1 + -2m + 3n Combine like terms: -3n + 3n = 0 0 = -1 + -2m + 3n Simplifying 0 = -1 + -2m + 3n The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
d = {0}
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