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Simplifying 5z + 2(3y + -2x) + 6(3x + 4y) + 10 = 0 Reorder the terms: 5z + 2(-2x + 3y) + 6(3x + 4y) + 10 = 0 5z + (-2x * 2 + 3y * 2) + 6(3x + 4y) + 10 = 0 5z + (-4x + 6y) + 6(3x + 4y) + 10 = 0 5z + -4x + 6y + (3x * 6 + 4y * 6) + 10 = 0 5z + -4x + 6y + (18x + 24y) + 10 = 0 Reorder the terms: 10 + -4x + 18x + 6y + 24y + 5z = 0 Combine like terms: -4x + 18x = 14x 10 + 14x + 6y + 24y + 5z = 0 Combine like terms: 6y + 24y = 30y 10 + 14x + 30y + 5z = 0 Solving 10 + 14x + 30y + 5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + 14x + 30y + -10 + 5z = 0 + -10 Reorder the terms: 10 + -10 + 14x + 30y + 5z = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 14x + 30y + 5z = 0 + -10 14x + 30y + 5z = 0 + -10 Combine like terms: 0 + -10 = -10 14x + 30y + 5z = -10 Add '-30y' to each side of the equation. 14x + 30y + -30y + 5z = -10 + -30y Combine like terms: 30y + -30y = 0 14x + 0 + 5z = -10 + -30y 14x + 5z = -10 + -30y Add '-5z' to each side of the equation. 14x + 5z + -5z = -10 + -30y + -5z Combine like terms: 5z + -5z = 0 14x + 0 = -10 + -30y + -5z 14x = -10 + -30y + -5z Divide each side by '14'. x = -0.7142857143 + -2.142857143y + -0.3571428571z Simplifying x = -0.7142857143 + -2.142857143y + -0.3571428571z
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