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Simplifying 6(x + -5y + -7z) = 0 (x * 6 + -5y * 6 + -7z * 6) = 0 (6x + -30y + -42z) = 0 Solving 6x + -30y + -42z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30y' to each side of the equation. 6x + -30y + 30y + -42z = 0 + 30y Combine like terms: -30y + 30y = 0 6x + 0 + -42z = 0 + 30y 6x + -42z = 0 + 30y Remove the zero: 6x + -42z = 30y Add '42z' to each side of the equation. 6x + -42z + 42z = 30y + 42z Combine like terms: -42z + 42z = 0 6x + 0 = 30y + 42z 6x = 30y + 42z Divide each side by '6'. x = 5y + 7z Simplifying x = 5y + 7z
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