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Simplifying 3(5x + -1y + 2z) + -2(-1x + y + -4z) = 0 (5x * 3 + -1y * 3 + 2z * 3) + -2(-1x + y + -4z) = 0 (15x + -3y + 6z) + -2(-1x + y + -4z) = 0 15x + -3y + 6z + (-1x * -2 + y * -2 + -4z * -2) = 0 15x + -3y + 6z + (2x + -2y + 8z) = 0 Reorder the terms: 15x + 2x + -3y + -2y + 6z + 8z = 0 Combine like terms: 15x + 2x = 17x 17x + -3y + -2y + 6z + 8z = 0 Combine like terms: -3y + -2y = -5y 17x + -5y + 6z + 8z = 0 Combine like terms: 6z + 8z = 14z 17x + -5y + 14z = 0 Solving 17x + -5y + 14z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 17x + -5y + 5y + 14z = 0 + 5y Combine like terms: -5y + 5y = 0 17x + 0 + 14z = 0 + 5y 17x + 14z = 0 + 5y Remove the zero: 17x + 14z = 5y Add '-14z' to each side of the equation. 17x + 14z + -14z = 5y + -14z Combine like terms: 14z + -14z = 0 17x + 0 = 5y + -14z 17x = 5y + -14z Divide each side by '17'. x = 0.2941176471y + -0.8235294118z Simplifying x = 0.2941176471y + -0.8235294118z
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