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Simplifying (5m + -4n)(5m + -4n) = 0 Multiply (5m + -4n) * (5m + -4n) (5m * (5m + -4n) + -4n * (5m + -4n)) = 0 ((5m * 5m + -4n * 5m) + -4n * (5m + -4n)) = 0 Reorder the terms: ((-20mn + 25m2) + -4n * (5m + -4n)) = 0 ((-20mn + 25m2) + -4n * (5m + -4n)) = 0 (-20mn + 25m2 + (5m * -4n + -4n * -4n)) = 0 (-20mn + 25m2 + (-20mn + 16n2)) = 0 Reorder the terms: (-20mn + -20mn + 25m2 + 16n2) = 0 Combine like terms: -20mn + -20mn = -40mn (-40mn + 25m2 + 16n2) = 0 Solving -40mn + 25m2 + 16n2 = 0 Solving for variable 'm'. Factor a trinomial. (5m + -4n)(5m + -4n) = 0Subproblem 1
Set the factor '(5m + -4n)' equal to zero and attempt to solve: Simplifying 5m + -4n = 0 Solving 5m + -4n = 0 Move all terms containing m to the left, all other terms to the right. Add '4n' to each side of the equation. 5m + -4n + 4n = 0 + 4n Combine like terms: -4n + 4n = 0 5m + 0 = 0 + 4n 5m = 0 + 4n Remove the zero: 5m = 4n Divide each side by '5'. m = 0.8n Simplifying m = 0.8nSubproblem 2
Set the factor '(5m + -4n)' equal to zero and attempt to solve: Simplifying 5m + -4n = 0 Solving 5m + -4n = 0 Move all terms containing m to the left, all other terms to the right. Add '4n' to each side of the equation. 5m + -4n + 4n = 0 + 4n Combine like terms: -4n + 4n = 0 5m + 0 = 0 + 4n 5m = 0 + 4n Remove the zero: 5m = 4n Divide each side by '5'. m = 0.8n Simplifying m = 0.8nSolution
m = {0.8n, 0.8n}
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