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Simplifying (12w + -2x + -9y + 6z) * 10 = 0 Reorder the terms for easier multiplication: 10(12w + -2x + -9y + 6z) = 0 (12w * 10 + -2x * 10 + -9y * 10 + 6z * 10) = 0 (120w + -20x + -90y + 60z) = 0 Solving 120w + -20x + -90y + 60z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '20x' to each side of the equation. 120w + -20x + -90y + 20x + 60z = 0 + 20x Reorder the terms: 120w + -20x + 20x + -90y + 60z = 0 + 20x Combine like terms: -20x + 20x = 0 120w + 0 + -90y + 60z = 0 + 20x 120w + -90y + 60z = 0 + 20x Remove the zero: 120w + -90y + 60z = 20x Add '90y' to each side of the equation. 120w + -90y + 90y + 60z = 20x + 90y Combine like terms: -90y + 90y = 0 120w + 0 + 60z = 20x + 90y 120w + 60z = 20x + 90y Add '-60z' to each side of the equation. 120w + 60z + -60z = 20x + 90y + -60z Combine like terms: 60z + -60z = 0 120w + 0 = 20x + 90y + -60z 120w = 20x + 90y + -60z Divide each side by '120'. w = 0.1666666667x + 0.75y + -0.5z Simplifying w = 0.1666666667x + 0.75y + -0.5z
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