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Simplifying 6(z + -6) + 5(3 + -2z) + z = 0 Reorder the terms: 6(-6 + z) + 5(3 + -2z) + z = 0 (-6 * 6 + z * 6) + 5(3 + -2z) + z = 0 (-36 + 6z) + 5(3 + -2z) + z = 0 -36 + 6z + (3 * 5 + -2z * 5) + z = 0 -36 + 6z + (15 + -10z) + z = 0 Reorder the terms: -36 + 15 + 6z + -10z + z = 0 Combine like terms: -36 + 15 = -21 -21 + 6z + -10z + z = 0 Combine like terms: 6z + -10z = -4z -21 + -4z + z = 0 Combine like terms: -4z + z = -3z -21 + -3z = 0 Solving -21 + -3z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + -3z = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -3z = 0 + 21 -3z = 0 + 21 Combine like terms: 0 + 21 = 21 -3z = 21 Divide each side by '-3'. z = -7 Simplifying z = -7
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