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Simplifying 4(3x + 5y + 2z) + 3(x + -1y) = 0 (3x * 4 + 5y * 4 + 2z * 4) + 3(x + -1y) = 0 (12x + 20y + 8z) + 3(x + -1y) = 0 12x + 20y + 8z + (x * 3 + -1y * 3) = 0 12x + 20y + 8z + (3x + -3y) = 0 Reorder the terms: 12x + 3x + 20y + -3y + 8z = 0 Combine like terms: 12x + 3x = 15x 15x + 20y + -3y + 8z = 0 Combine like terms: 20y + -3y = 17y 15x + 17y + 8z = 0 Solving 15x + 17y + 8z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17y' to each side of the equation. 15x + 17y + -17y + 8z = 0 + -17y Combine like terms: 17y + -17y = 0 15x + 0 + 8z = 0 + -17y 15x + 8z = 0 + -17y Remove the zero: 15x + 8z = -17y Add '-8z' to each side of the equation. 15x + 8z + -8z = -17y + -8z Combine like terms: 8z + -8z = 0 15x + 0 = -17y + -8z 15x = -17y + -8z Divide each side by '15'. x = -1.133333333y + -0.5333333333z Simplifying x = -1.133333333y + -0.5333333333z
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