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Simplifying (2y + -4x + -3) + -1(2y + -4x + -3z + -1) = 0 Reorder the terms: (-3 + -4x + 2y) + -1(2y + -4x + -3z + -1) = 0 Remove parenthesis around (-3 + -4x + 2y) -3 + -4x + 2y + -1(2y + -4x + -3z + -1) = 0 Reorder the terms: -3 + -4x + 2y + -1(-1 + -4x + 2y + -3z) = 0 -3 + -4x + 2y + (-1 * -1 + -4x * -1 + 2y * -1 + -3z * -1) = 0 -3 + -4x + 2y + (1 + 4x + -2y + 3z) = 0 Reorder the terms: -3 + 1 + -4x + 4x + 2y + -2y + 3z = 0 Combine like terms: -3 + 1 = -2 -2 + -4x + 4x + 2y + -2y + 3z = 0 Combine like terms: -4x + 4x = 0 -2 + 0 + 2y + -2y + 3z = 0 -2 + 2y + -2y + 3z = 0 Combine like terms: 2y + -2y = 0 -2 + 0 + 3z = 0 -2 + 3z = 0 Solving -2 + 3z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3z = 0 + 2 3z = 0 + 2 Combine like terms: 0 + 2 = 2 3z = 2 Divide each side by '3'. z = 0.6666666667 Simplifying z = 0.6666666667
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