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Simplifying 5(6 + 3x + 4y) + 3(9z + 3x + 5y) = 0 (6 * 5 + 3x * 5 + 4y * 5) + 3(9z + 3x + 5y) = 0 (30 + 15x + 20y) + 3(9z + 3x + 5y) = 0 Reorder the terms: 30 + 15x + 20y + 3(3x + 5y + 9z) = 0 30 + 15x + 20y + (3x * 3 + 5y * 3 + 9z * 3) = 0 30 + 15x + 20y + (9x + 15y + 27z) = 0 Reorder the terms: 30 + 15x + 9x + 20y + 15y + 27z = 0 Combine like terms: 15x + 9x = 24x 30 + 24x + 20y + 15y + 27z = 0 Combine like terms: 20y + 15y = 35y 30 + 24x + 35y + 27z = 0 Solving 30 + 24x + 35y + 27z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + 24x + 35y + -30 + 27z = 0 + -30 Reorder the terms: 30 + -30 + 24x + 35y + 27z = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 24x + 35y + 27z = 0 + -30 24x + 35y + 27z = 0 + -30 Combine like terms: 0 + -30 = -30 24x + 35y + 27z = -30 Add '-35y' to each side of the equation. 24x + 35y + -35y + 27z = -30 + -35y Combine like terms: 35y + -35y = 0 24x + 0 + 27z = -30 + -35y 24x + 27z = -30 + -35y Add '-27z' to each side of the equation. 24x + 27z + -27z = -30 + -35y + -27z Combine like terms: 27z + -27z = 0 24x + 0 = -30 + -35y + -27z 24x = -30 + -35y + -27z Divide each side by '24'. x = -1.25 + -1.458333333y + -1.125z Simplifying x = -1.25 + -1.458333333y + -1.125z
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