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