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Simplifying -5(-2z) + 4(3 + -2) + -7(3 + z) = 0 Remove parenthesis around (-2z) -5 * -2z + 4(3 + -2) + -7(3 + z) = 0 Multiply -5 * -2 10z + 4(3 + -2) + -7(3 + z) = 0 Combine like terms: 3 + -2 = 1 10z + 4(1) + -7(3 + z) = 0 Multiply 4 * 1 10z + 4 + -7(3 + z) = 0 10z + 4 + (3 * -7 + z * -7) = 0 10z + 4 + (-21 + -7z) = 0 Reorder the terms: 4 + -21 + 10z + -7z = 0 Combine like terms: 4 + -21 = -17 -17 + 10z + -7z = 0 Combine like terms: 10z + -7z = 3z -17 + 3z = 0 Solving -17 + 3z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + 3z = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 3z = 0 + 17 3z = 0 + 17 Combine like terms: 0 + 17 = 17 3z = 17 Divide each side by '3'. z = 5.666666667 Simplifying z = 5.666666667
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