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Simplifying if(x + m)(x + n) = (x2 + 6x + 5) * find(m2 + n2) Reorder the terms: fi(m + x)(x + n) = (x2 + 6x + 5) * find(m2 + n2) Reorder the terms: fi(m + x)(n + x) = (x2 + 6x + 5) * find(m2 + n2) Multiply (m + x) * (n + x) fi(m(n + x) + x(n + x)) = (x2 + 6x + 5) * find(m2 + n2) fi((n * m + x * m) + x(n + x)) = (x2 + 6x + 5) * find(m2 + n2) fi((mn + mx) + x(n + x)) = (x2 + 6x + 5) * find(m2 + n2) fi(mn + mx + (n * x + x * x)) = (x2 + 6x + 5) * find(m2 + n2) fi(mn + mx + (nx + x2)) = (x2 + 6x + 5) * find(m2 + n2) fi(mn + mx + nx + x2) = (x2 + 6x + 5) * find(m2 + n2) (mn * fi + mx * fi + nx * fi + x2 * fi) = (x2 + 6x + 5) * find(m2 + n2) (fimn + fimx + finx + fix2) = (x2 + 6x + 5) * find(m2 + n2) Reorder the terms: fimn + fimx + finx + fix2 = (5 + 6x + x2) * find(m2 + n2) Reorder the terms for easier multiplication: fimn + fimx + finx + fix2 = dfin(5 + 6x + x2)(m2 + n2) Multiply (5 + 6x + x2) * (m2 + n2) fimn + fimx + finx + fix2 = dfin(5(m2 + n2) + 6x * (m2 + n2) + x2(m2 + n2)) fimn + fimx + finx + fix2 = dfin((m2 * 5 + n2 * 5) + 6x * (m2 + n2) + x2(m2 + n2)) fimn + fimx + finx + fix2 = dfin((5m2 + 5n2) + 6x * (m2 + n2) + x2(m2 + n2)) fimn + fimx + finx + fix2 = dfin(5m2 + 5n2 + (m2 * 6x + n2 * 6x) + x2(m2 + n2)) fimn + fimx + finx + fix2 = dfin(5m2 + 5n2 + (6m2x + 6n2x) + x2(m2 + n2)) fimn + fimx + finx + fix2 = dfin(5m2 + 5n2 + 6m2x + 6n2x + (m2 * x2 + n2 * x2)) fimn + fimx + finx + fix2 = dfin(5m2 + 5n2 + 6m2x + 6n2x + (m2x2 + n2x2)) Reorder the terms: fimn + fimx + finx + fix2 = dfin(5m2 + 6m2x + m2x2 + 5n2 + 6n2x + n2x2) fimn + fimx + finx + fix2 = dfin(5m2 + 6m2x + m2x2 + 5n2 + 6n2x + n2x2) fimn + fimx + finx + fix2 = (5m2 * dfin + 6m2x * dfin + m2x2 * dfin + 5n2 * dfin + 6n2x * dfin + n2x2 * dfin) fimn + fimx + finx + fix2 = (5dfim2n + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2) Solving fimn + fimx + finx + fix2 = 5dfim2n + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Add '-5dfim2n' to each side of the equation. fimn + fimx + finx + -5dfim2n + fix2 = 5dfim2n + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + -5dfim2n + dfin3x2 Reorder the terms: -5dfim2n + fimn + fimx + finx + fix2 = 5dfim2n + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + -5dfim2n + dfin3x2 Reorder the terms: -5dfim2n + fimn + fimx + finx + fix2 = 5dfim2n + -5dfim2n + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Combine like terms: 5dfim2n + -5dfim2n = 0 -5dfim2n + fimn + fimx + finx + fix2 = 0 + 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 -5dfim2n + fimn + fimx + finx + fix2 = 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Add '-6dfim2nx' to each side of the equation. -5dfim2n + fimn + fimx + finx + -6dfim2nx + fix2 = 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + -6dfim2nx + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + fimn + fimx + finx + fix2 = 6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + -6dfim2nx + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + fimn + fimx + finx + fix2 = 6dfim2nx + -6dfim2nx + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Combine like terms: 6dfim2nx + -6dfim2nx = 0 -5dfim2n + -6dfim2nx + fimn + fimx + finx + fix2 = 0 + dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 -5dfim2n + -6dfim2nx + fimn + fimx + finx + fix2 = dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Add '-1dfim2nx2' to each side of the equation. -5dfim2n + -6dfim2nx + fimn + fimx + finx + -1dfim2nx2 + fix2 = dfim2nx2 + 5dfin3 + 6dfin3x + -1dfim2nx2 + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + fimn + fimx + finx + fix2 = dfim2nx2 + 5dfin3 + 6dfin3x + -1dfim2nx2 + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + fimn + fimx + finx + fix2 = dfim2nx2 + -1dfim2nx2 + 5dfin3 + 6dfin3x + dfin3x2 Combine like terms: dfim2nx2 + -1dfim2nx2 = 0 -5dfim2n + -6dfim2nx + -1dfim2nx2 + fimn + fimx + finx + fix2 = 0 + 5dfin3 + 6dfin3x + dfin3x2 -5dfim2n + -6dfim2nx + -1dfim2nx2 + fimn + fimx + finx + fix2 = 5dfin3 + 6dfin3x + dfin3x2 Add '-5dfin3' to each side of the equation. -5dfim2n + -6dfim2nx + -1dfim2nx2 + fimn + fimx + finx + -5dfin3 + fix2 = 5dfin3 + 6dfin3x + -5dfin3 + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + fimn + fimx + finx + fix2 = 5dfin3 + 6dfin3x + -5dfin3 + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + fimn + fimx + finx + fix2 = 5dfin3 + -5dfin3 + 6dfin3x + dfin3x2 Combine like terms: 5dfin3 + -5dfin3 = 0 -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + fimn + fimx + finx + fix2 = 0 + 6dfin3x + dfin3x2 -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + fimn + fimx + finx + fix2 = 6dfin3x + dfin3x2 Add '-6dfin3x' to each side of the equation. -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + fimn + fimx + finx + -6dfin3x + fix2 = 6dfin3x + -6dfin3x + dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + fimn + fimx + finx + fix2 = 6dfin3x + -6dfin3x + dfin3x2 Combine like terms: 6dfin3x + -6dfin3x = 0 -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + fimn + fimx + finx + fix2 = 0 + dfin3x2 -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + fimn + fimx + finx + fix2 = dfin3x2 Add '-1dfin3x2' to each side of the equation. -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + fimn + fimx + finx + -1dfin3x2 + fix2 = dfin3x2 + -1dfin3x2 Reorder the terms: -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + -1dfin3x2 + fimn + fimx + finx + fix2 = dfin3x2 + -1dfin3x2 Combine like terms: dfin3x2 + -1dfin3x2 = 0 -5dfim2n + -6dfim2nx + -1dfim2nx2 + -5dfin3 + -6dfin3x + -1dfin3x2 + fimn + fimx + finx + fix2 = 0 Factor out the Greatest Common Factor (GCF), 'fi'. fi(-5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2) = 0Subproblem 1
Set the factor 'fi' equal to zero and attempt to solve: Simplifying fi = 0 Solving fi = 0 Move all terms containing f to the left, all other terms to the right. Simplifying fi = 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 '(-5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2)' equal to zero and attempt to solve: Simplifying -5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 0 Solving -5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 0 Move all terms containing f to the left, all other terms to the right. Add '5dm2n' to each side of the equation. -5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + 5dm2n + x2 = 0 + 5dm2n Reorder the terms: -5dm2n + 5dm2n + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 0 + 5dm2n Combine like terms: -5dm2n + 5dm2n = 0 0 + -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 0 + 5dm2n -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 0 + 5dm2n Remove the zero: -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n Add '6dm2nx' to each side of the equation. -6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + 6dm2nx + x2 = 5dm2n + 6dm2nx Reorder the terms: -6dm2nx + 6dm2nx + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx Combine like terms: -6dm2nx + 6dm2nx = 0 0 + -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx Add 'dm2nx2' to each side of the equation. -1dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + dm2nx2 + x2 = 5dm2n + 6dm2nx + dm2nx2 Reorder the terms: -1dm2nx2 + dm2nx2 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 Combine like terms: -1dm2nx2 + dm2nx2 = 0 0 + -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 Add '5dn3' to each side of the equation. -5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + 5dn3 + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 Reorder the terms: -5dn3 + 5dn3 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 Combine like terms: -5dn3 + 5dn3 = 0 0 + -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 -6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 Add '6dn3x' to each side of the equation. -6dn3x + -1dn3x2 + mn + mx + nx + 6dn3x + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x Reorder the terms: -6dn3x + 6dn3x + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x Combine like terms: -6dn3x + 6dn3x = 0 0 + -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x -1dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x Add 'dn3x2' to each side of the equation. -1dn3x2 + mn + mx + nx + dn3x2 + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 Reorder the terms: -1dn3x2 + dn3x2 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 Combine like terms: -1dn3x2 + dn3x2 = 0 0 + mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 Add '-1mn' to each side of the equation. mn + mx + nx + -1mn + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn Reorder the terms: mn + -1mn + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn Combine like terms: mn + -1mn = 0 0 + mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn Add '-1mx' to each side of the equation. mx + nx + -1mx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx Reorder the terms: mx + -1mx + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx Combine like terms: mx + -1mx = 0 0 + nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx Add '-1nx' to each side of the equation. nx + -1nx + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx Combine like terms: nx + -1nx = 0 0 + x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx Add '-1x2' to each side of the equation. x2 + -1x2 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx + -1x2 Combine like terms: x2 + -1x2 = 0 0 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx + -1x2 Simplifying 0 = 5dm2n + 6dm2nx + dm2nx2 + 5dn3 + 6dn3x + dn3x2 + -1mn + -1mx + -1nx + -1x2 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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