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Simplifying Mod(x2 + 6x + 8) = mod(x2 + 4x + 5) + mod(2x + 3) Reorder the terms: doM(8 + 6x + x2) = mod(x2 + 4x + 5) + mod(2x + 3) (8 * doM + 6x * doM + x2 * doM) = mod(x2 + 4x + 5) + mod(2x + 3) (8doM + 6doxM + dox2M) = mod(x2 + 4x + 5) + mod(2x + 3) Reorder the terms: 8doM + 6doxM + dox2M = dmo(5 + 4x + x2) + mod(2x + 3) 8doM + 6doxM + dox2M = (5 * dmo + 4x * dmo + x2 * dmo) + mod(2x + 3) 8doM + 6doxM + dox2M = (5dmo + 4dmox + dmox2) + mod(2x + 3) Reorder the terms: 8doM + 6doxM + dox2M = 5dmo + 4dmox + dmox2 + dmo(3 + 2x) 8doM + 6doxM + dox2M = 5dmo + 4dmox + dmox2 + (3 * dmo + 2x * dmo) 8doM + 6doxM + dox2M = 5dmo + 4dmox + dmox2 + (3dmo + 2dmox) Reorder the terms: 8doM + 6doxM + dox2M = 5dmo + 3dmo + 4dmox + 2dmox + dmox2 Combine like terms: 5dmo + 3dmo = 8dmo 8doM + 6doxM + dox2M = 8dmo + 4dmox + 2dmox + dmox2 Combine like terms: 4dmox + 2dmox = 6dmox 8doM + 6doxM + dox2M = 8dmo + 6dmox + dmox2 Solving 8doM + 6doxM + dox2M = 8dmo + 6dmox + dmox2 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8dmo' to each side of the equation. 8doM + 6doxM + -8dmo + dox2M = 8dmo + 6dmox + -8dmo + dmox2 Reorder the terms: -8dmo + 8doM + 6doxM + dox2M = 8dmo + 6dmox + -8dmo + dmox2 Reorder the terms: -8dmo + 8doM + 6doxM + dox2M = 8dmo + -8dmo + 6dmox + dmox2 Combine like terms: 8dmo + -8dmo = 0 -8dmo + 8doM + 6doxM + dox2M = 0 + 6dmox + dmox2 -8dmo + 8doM + 6doxM + dox2M = 6dmox + dmox2 Add '-6dmox' to each side of the equation. -8dmo + 8doM + 6doxM + -6dmox + dox2M = 6dmox + -6dmox + dmox2 Reorder the terms: -8dmo + -6dmox + 8doM + 6doxM + dox2M = 6dmox + -6dmox + dmox2 Combine like terms: 6dmox + -6dmox = 0 -8dmo + -6dmox + 8doM + 6doxM + dox2M = 0 + dmox2 -8dmo + -6dmox + 8doM + 6doxM + dox2M = dmox2 Add '-1dmox2' to each side of the equation. -8dmo + -6dmox + 8doM + 6doxM + -1dmox2 + dox2M = dmox2 + -1dmox2 Reorder the terms: -8dmo + -6dmox + -1dmox2 + 8doM + 6doxM + dox2M = dmox2 + -1dmox2 Combine like terms: dmox2 + -1dmox2 = 0 -8dmo + -6dmox + -1dmox2 + 8doM + 6doxM + dox2M = 0 Factor out the Greatest Common Factor (GCF), 'do'. do(-8m + -6mx + -1mx2 + 8M + 6xM + x2M) = 0Subproblem 1
Set the factor 'do' equal to zero and attempt to solve: Simplifying do = 0 Solving do = 0 Move all terms containing d to the left, all other terms to the right. Simplifying do = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-8m + -6mx + -1mx2 + 8M + 6xM + x2M)' equal to zero and attempt to solve: Simplifying -8m + -6mx + -1mx2 + 8M + 6xM + x2M = 0 Reorder the terms: 8M + -8m + -6mx + -1mx2 + 6xM + x2M = 0 Solving 8M + -8m + -6mx + -1mx2 + 6xM + x2M = 0 Move all terms containing d to the left, all other terms to the right. Add '-8M' to each side of the equation. 8M + -8m + -6mx + -1mx2 + 6xM + -8M + x2M = 0 + -8M Reorder the terms: 8M + -8M + -8m + -6mx + -1mx2 + 6xM + x2M = 0 + -8M Combine like terms: 8M + -8M = 0 0 + -8m + -6mx + -1mx2 + 6xM + x2M = 0 + -8M -8m + -6mx + -1mx2 + 6xM + x2M = 0 + -8M Remove the zero: -8m + -6mx + -1mx2 + 6xM + x2M = -8M Add '8m' to each side of the equation. -8m + -6mx + -1mx2 + 6xM + 8m + x2M = -8M + 8m Reorder the terms: -8m + 8m + -6mx + -1mx2 + 6xM + x2M = -8M + 8m Combine like terms: -8m + 8m = 0 0 + -6mx + -1mx2 + 6xM + x2M = -8M + 8m -6mx + -1mx2 + 6xM + x2M = -8M + 8m Add '6mx' to each side of the equation. -6mx + -1mx2 + 6xM + 6mx + x2M = -8M + 8m + 6mx Reorder the terms: -6mx + 6mx + -1mx2 + 6xM + x2M = -8M + 8m + 6mx Combine like terms: -6mx + 6mx = 0 0 + -1mx2 + 6xM + x2M = -8M + 8m + 6mx -1mx2 + 6xM + x2M = -8M + 8m + 6mx Add 'mx2' to each side of the equation. -1mx2 + 6xM + mx2 + x2M = -8M + 8m + 6mx + mx2 Reorder the terms: -1mx2 + mx2 + 6xM + x2M = -8M + 8m + 6mx + mx2 Combine like terms: -1mx2 + mx2 = 0 0 + 6xM + x2M = -8M + 8m + 6mx + mx2 6xM + x2M = -8M + 8m + 6mx + mx2 Add '-6xM' to each side of the equation. 6xM + -6xM + x2M = -8M + 8m + 6mx + mx2 + -6xM Combine like terms: 6xM + -6xM = 0 0 + x2M = -8M + 8m + 6mx + mx2 + -6xM x2M = -8M + 8m + 6mx + mx2 + -6xM Add '-1x2M' to each side of the equation. x2M + -1x2M = -8M + 8m + 6mx + mx2 + -6xM + -1x2M Combine like terms: x2M + -1x2M = 0 0 = -8M + 8m + 6mx + mx2 + -6xM + -1x2M Simplifying 0 = -8M + 8m + 6mx + mx2 + -6xM + -1x2M 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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