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Simplifying 10(z + 3) + -4(z + -4) + 3(z + -3) = 0 Reorder the terms: 10(3 + z) + -4(z + -4) + 3(z + -3) = 0 (3 * 10 + z * 10) + -4(z + -4) + 3(z + -3) = 0 (30 + 10z) + -4(z + -4) + 3(z + -3) = 0 Reorder the terms: 30 + 10z + -4(-4 + z) + 3(z + -3) = 0 30 + 10z + (-4 * -4 + z * -4) + 3(z + -3) = 0 30 + 10z + (16 + -4z) + 3(z + -3) = 0 Reorder the terms: 30 + 10z + 16 + -4z + 3(-3 + z) = 0 30 + 10z + 16 + -4z + (-3 * 3 + z * 3) = 0 30 + 10z + 16 + -4z + (-9 + 3z) = 0 Reorder the terms: 30 + 16 + -9 + 10z + -4z + 3z = 0 Combine like terms: 30 + 16 = 46 46 + -9 + 10z + -4z + 3z = 0 Combine like terms: 46 + -9 = 37 37 + 10z + -4z + 3z = 0 Combine like terms: 10z + -4z = 6z 37 + 6z + 3z = 0 Combine like terms: 6z + 3z = 9z 37 + 9z = 0 Solving 37 + 9z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + 9z = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 9z = 0 + -37 9z = 0 + -37 Combine like terms: 0 + -37 = -37 9z = -37 Divide each side by '9'. z = -4.111111111 Simplifying z = -4.111111111
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