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Simplifying 5(2x + 3y) + 2(x + 6y) = 0 (2x * 5 + 3y * 5) + 2(x + 6y) = 0 (10x + 15y) + 2(x + 6y) = 0 10x + 15y + (x * 2 + 6y * 2) = 0 10x + 15y + (2x + 12y) = 0 Reorder the terms: 10x + 2x + 15y + 12y = 0 Combine like terms: 10x + 2x = 12x 12x + 15y + 12y = 0 Combine like terms: 15y + 12y = 27y 12x + 27y = 0 Solving 12x + 27y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27y' to each side of the equation. 12x + 27y + -27y = 0 + -27y Combine like terms: 27y + -27y = 0 12x + 0 = 0 + -27y 12x = 0 + -27y Remove the zero: 12x = -27y Divide each side by '12'. x = -2.25y Simplifying x = -2.25y
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