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Simplifying -10(z + 3) + 5(3z + -6) = 4(z + -4) + 10 Reorder the terms: -10(3 + z) + 5(3z + -6) = 4(z + -4) + 10 (3 * -10 + z * -10) + 5(3z + -6) = 4(z + -4) + 10 (-30 + -10z) + 5(3z + -6) = 4(z + -4) + 10 Reorder the terms: -30 + -10z + 5(-6 + 3z) = 4(z + -4) + 10 -30 + -10z + (-6 * 5 + 3z * 5) = 4(z + -4) + 10 -30 + -10z + (-30 + 15z) = 4(z + -4) + 10 Reorder the terms: -30 + -30 + -10z + 15z = 4(z + -4) + 10 Combine like terms: -30 + -30 = -60 -60 + -10z + 15z = 4(z + -4) + 10 Combine like terms: -10z + 15z = 5z -60 + 5z = 4(z + -4) + 10 Reorder the terms: -60 + 5z = 4(-4 + z) + 10 -60 + 5z = (-4 * 4 + z * 4) + 10 -60 + 5z = (-16 + 4z) + 10 Reorder the terms: -60 + 5z = -16 + 10 + 4z Combine like terms: -16 + 10 = -6 -60 + 5z = -6 + 4z Solving -60 + 5z = -6 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -60 + 5z + -4z = -6 + 4z + -4z Combine like terms: 5z + -4z = 1z -60 + 1z = -6 + 4z + -4z Combine like terms: 4z + -4z = 0 -60 + 1z = -6 + 0 -60 + 1z = -6 Add '60' to each side of the equation. -60 + 60 + 1z = -6 + 60 Combine like terms: -60 + 60 = 0 0 + 1z = -6 + 60 1z = -6 + 60 Combine like terms: -6 + 60 = 54 1z = 54 Divide each side by '1'. z = 54 Simplifying z = 54
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