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Simplifying -6n(5m + 9) + (-2m)(-3n) = 0 Reorder the terms: -6n(9 + 5m) + (-2m)(-3n) = 0 (9 * -6n + 5m * -6n) + (-2m)(-3n) = 0 Reorder the terms: (-30mn + -54n) + (-2m)(-3n) = 0 (-30mn + -54n) + (-2m)(-3n) = 0 Remove parenthesis around (-2m) -30mn + -54n + -2m(-3n) = 0 Remove parenthesis around (-3n) -30mn + -54n + -2m * -3n = 0 Reorder the terms for easier multiplication: -30mn + -54n + -2 * -3m * n = 0 Multiply -2 * -3 -30mn + -54n + 6m * n = 0 Multiply m * n -30mn + -54n + 6mn = 0 Reorder the terms: -30mn + 6mn + -54n = 0 Combine like terms: -30mn + 6mn = -24mn -24mn + -54n = 0 Solving -24mn + -54n = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '54n' to each side of the equation. -24mn + -54n + 54n = 0 + 54n Combine like terms: -54n + 54n = 0 -24mn + 0 = 0 + 54n -24mn = 0 + 54n Remove the zero: -24mn = 54n Divide each side by '-24n'. m = -2.25 Simplifying m = -2.25
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