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Simplifying 4(3x + 5y) + 2z + 3(x + -1z) = 0 (3x * 4 + 5y * 4) + 2z + 3(x + -1z) = 0 (12x + 20y) + 2z + 3(x + -1z) = 0 12x + 20y + 2z + (x * 3 + -1z * 3) = 0 12x + 20y + 2z + (3x + -3z) = 0 Reorder the terms: 12x + 3x + 20y + 2z + -3z = 0 Combine like terms: 12x + 3x = 15x 15x + 20y + 2z + -3z = 0 Combine like terms: 2z + -3z = -1z 15x + 20y + -1z = 0 Solving 15x + 20y + -1z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20y' to each side of the equation. 15x + 20y + -20y + -1z = 0 + -20y Combine like terms: 20y + -20y = 0 15x + 0 + -1z = 0 + -20y 15x + -1z = 0 + -20y Remove the zero: 15x + -1z = -20y Add 'z' to each side of the equation. 15x + -1z + z = -20y + z Combine like terms: -1z + z = 0 15x + 0 = -20y + z 15x = -20y + z Divide each side by '15'. x = -1.333333333y + 0.06666666667z Simplifying x = -1.333333333y + 0.06666666667z
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