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Simplifying -10(z + 3) + 4(4z + -4) = 5(z + -5) + 12 Reorder the terms: -10(3 + z) + 4(4z + -4) = 5(z + -5) + 12 (3 * -10 + z * -10) + 4(4z + -4) = 5(z + -5) + 12 (-30 + -10z) + 4(4z + -4) = 5(z + -5) + 12 Reorder the terms: -30 + -10z + 4(-4 + 4z) = 5(z + -5) + 12 -30 + -10z + (-4 * 4 + 4z * 4) = 5(z + -5) + 12 -30 + -10z + (-16 + 16z) = 5(z + -5) + 12 Reorder the terms: -30 + -16 + -10z + 16z = 5(z + -5) + 12 Combine like terms: -30 + -16 = -46 -46 + -10z + 16z = 5(z + -5) + 12 Combine like terms: -10z + 16z = 6z -46 + 6z = 5(z + -5) + 12 Reorder the terms: -46 + 6z = 5(-5 + z) + 12 -46 + 6z = (-5 * 5 + z * 5) + 12 -46 + 6z = (-25 + 5z) + 12 Reorder the terms: -46 + 6z = -25 + 12 + 5z Combine like terms: -25 + 12 = -13 -46 + 6z = -13 + 5z Solving -46 + 6z = -13 + 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. -46 + 6z + -5z = -13 + 5z + -5z Combine like terms: 6z + -5z = 1z -46 + 1z = -13 + 5z + -5z Combine like terms: 5z + -5z = 0 -46 + 1z = -13 + 0 -46 + 1z = -13 Add '46' to each side of the equation. -46 + 46 + 1z = -13 + 46 Combine like terms: -46 + 46 = 0 0 + 1z = -13 + 46 1z = -13 + 46 Combine like terms: -13 + 46 = 33 1z = 33 Divide each side by '1'. z = 33 Simplifying z = 33
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