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Simplifying 13(z + -4) + -3(z + -9) + -5(z + 4) = 0 Reorder the terms: 13(-4 + z) + -3(z + -9) + -5(z + 4) = 0 (-4 * 13 + z * 13) + -3(z + -9) + -5(z + 4) = 0 (-52 + 13z) + -3(z + -9) + -5(z + 4) = 0 Reorder the terms: -52 + 13z + -3(-9 + z) + -5(z + 4) = 0 -52 + 13z + (-9 * -3 + z * -3) + -5(z + 4) = 0 -52 + 13z + (27 + -3z) + -5(z + 4) = 0 Reorder the terms: -52 + 13z + 27 + -3z + -5(4 + z) = 0 -52 + 13z + 27 + -3z + (4 * -5 + z * -5) = 0 -52 + 13z + 27 + -3z + (-20 + -5z) = 0 Reorder the terms: -52 + 27 + -20 + 13z + -3z + -5z = 0 Combine like terms: -52 + 27 = -25 -25 + -20 + 13z + -3z + -5z = 0 Combine like terms: -25 + -20 = -45 -45 + 13z + -3z + -5z = 0 Combine like terms: 13z + -3z = 10z -45 + 10z + -5z = 0 Combine like terms: 10z + -5z = 5z -45 + 5z = 0 Solving -45 + 5z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '45' to each side of the equation. -45 + 45 + 5z = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 5z = 0 + 45 5z = 0 + 45 Combine like terms: 0 + 45 = 45 5z = 45 Divide each side by '5'. z = 9 Simplifying z = 9
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