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Simplifying 4mp + -6np + 8m + -12n = 0 Reorder the terms: 8m + 4mp + -12n + -6np = 0 Solving 8m + 4mp + -12n + -6np = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '12n' to each side of the equation. 8m + 4mp + -12n + 12n + -6np = 0 + 12n Combine like terms: -12n + 12n = 0 8m + 4mp + 0 + -6np = 0 + 12n 8m + 4mp + -6np = 0 + 12n Remove the zero: 8m + 4mp + -6np = 12n Add '6np' to each side of the equation. 8m + 4mp + -6np + 6np = 12n + 6np Combine like terms: -6np + 6np = 0 8m + 4mp + 0 = 12n + 6np 8m + 4mp = 12n + 6np Reorder the terms: 8m + 4mp + -12n + -6np = 12n + -12n + 6np + -6np Combine like terms: 12n + -12n = 0 8m + 4mp + -12n + -6np = 0 + 6np + -6np 8m + 4mp + -12n + -6np = 6np + -6np Combine like terms: 6np + -6np = 0 8m + 4mp + -12n + -6np = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4m + 2mp + -6n + -3np) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4m + 2mp + -6n + -3np)' equal to zero and attempt to solve: Simplifying 4m + 2mp + -6n + -3np = 0 Solving 4m + 2mp + -6n + -3np = 0 Move all terms containing m to the left, all other terms to the right. Add '6n' to each side of the equation. 4m + 2mp + -6n + 6n + -3np = 0 + 6n Combine like terms: -6n + 6n = 0 4m + 2mp + 0 + -3np = 0 + 6n 4m + 2mp + -3np = 0 + 6n Remove the zero: 4m + 2mp + -3np = 6n Add '3np' to each side of the equation. 4m + 2mp + -3np + 3np = 6n + 3np Combine like terms: -3np + 3np = 0 4m + 2mp + 0 = 6n + 3np 4m + 2mp = 6n + 3np 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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