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Simplifying -10(z + 3) + 4(4z + -6) = 5(z + -4) + 8 Reorder the terms: -10(3 + z) + 4(4z + -6) = 5(z + -4) + 8 (3 * -10 + z * -10) + 4(4z + -6) = 5(z + -4) + 8 (-30 + -10z) + 4(4z + -6) = 5(z + -4) + 8 Reorder the terms: -30 + -10z + 4(-6 + 4z) = 5(z + -4) + 8 -30 + -10z + (-6 * 4 + 4z * 4) = 5(z + -4) + 8 -30 + -10z + (-24 + 16z) = 5(z + -4) + 8 Reorder the terms: -30 + -24 + -10z + 16z = 5(z + -4) + 8 Combine like terms: -30 + -24 = -54 -54 + -10z + 16z = 5(z + -4) + 8 Combine like terms: -10z + 16z = 6z -54 + 6z = 5(z + -4) + 8 Reorder the terms: -54 + 6z = 5(-4 + z) + 8 -54 + 6z = (-4 * 5 + z * 5) + 8 -54 + 6z = (-20 + 5z) + 8 Reorder the terms: -54 + 6z = -20 + 8 + 5z Combine like terms: -20 + 8 = -12 -54 + 6z = -12 + 5z Solving -54 + 6z = -12 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -54 + 6z + -5z = -12 + 5z + -5z Combine like terms: 6z + -5z = 1z -54 + 1z = -12 + 5z + -5z Combine like terms: 5z + -5z = 0 -54 + 1z = -12 + 0 -54 + 1z = -12 Add '54' to each side of the equation. -54 + 54 + 1z = -12 + 54 Combine like terms: -54 + 54 = 0 0 + 1z = -12 + 54 1z = -12 + 54 Combine like terms: -12 + 54 = 42 1z = 42 Divide each side by '1'. z = 42 Simplifying z = 42
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