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Simplifying 4(3 + 3y + 2z) + 3(x + -1z) = 0 (3 * 4 + 3y * 4 + 2z * 4) + 3(x + -1z) = 0 (12 + 12y + 8z) + 3(x + -1z) = 0 12 + 12y + 8z + (x * 3 + -1z * 3) = 0 12 + 12y + 8z + (3x + -3z) = 0 Reorder the terms: 12 + 3x + 12y + 8z + -3z = 0 Combine like terms: 8z + -3z = 5z 12 + 3x + 12y + 5z = 0 Solving 12 + 3x + 12y + 5z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 3x + 12y + -12 + 5z = 0 + -12 Reorder the terms: 12 + -12 + 3x + 12y + 5z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 3x + 12y + 5z = 0 + -12 3x + 12y + 5z = 0 + -12 Combine like terms: 0 + -12 = -12 3x + 12y + 5z = -12 Add '-12y' to each side of the equation. 3x + 12y + -12y + 5z = -12 + -12y Combine like terms: 12y + -12y = 0 3x + 0 + 5z = -12 + -12y 3x + 5z = -12 + -12y Add '-5z' to each side of the equation. 3x + 5z + -5z = -12 + -12y + -5z Combine like terms: 5z + -5z = 0 3x + 0 = -12 + -12y + -5z 3x = -12 + -12y + -5z Divide each side by '3'. x = -4 + -4y + -1.666666667z Simplifying x = -4 + -4y + -1.666666667z
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