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Simplifying -19(z + 3) + 6(4z + -3) = 4(z + -5) + 12 Reorder the terms: -19(3 + z) + 6(4z + -3) = 4(z + -5) + 12 (3 * -19 + z * -19) + 6(4z + -3) = 4(z + -5) + 12 (-57 + -19z) + 6(4z + -3) = 4(z + -5) + 12 Reorder the terms: -57 + -19z + 6(-3 + 4z) = 4(z + -5) + 12 -57 + -19z + (-3 * 6 + 4z * 6) = 4(z + -5) + 12 -57 + -19z + (-18 + 24z) = 4(z + -5) + 12 Reorder the terms: -57 + -18 + -19z + 24z = 4(z + -5) + 12 Combine like terms: -57 + -18 = -75 -75 + -19z + 24z = 4(z + -5) + 12 Combine like terms: -19z + 24z = 5z -75 + 5z = 4(z + -5) + 12 Reorder the terms: -75 + 5z = 4(-5 + z) + 12 -75 + 5z = (-5 * 4 + z * 4) + 12 -75 + 5z = (-20 + 4z) + 12 Reorder the terms: -75 + 5z = -20 + 12 + 4z Combine like terms: -20 + 12 = -8 -75 + 5z = -8 + 4z Solving -75 + 5z = -8 + 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. -75 + 5z + -4z = -8 + 4z + -4z Combine like terms: 5z + -4z = 1z -75 + 1z = -8 + 4z + -4z Combine like terms: 4z + -4z = 0 -75 + 1z = -8 + 0 -75 + 1z = -8 Add '75' to each side of the equation. -75 + 75 + 1z = -8 + 75 Combine like terms: -75 + 75 = 0 0 + 1z = -8 + 75 1z = -8 + 75 Combine like terms: -8 + 75 = 67 1z = 67 Divide each side by '1'. z = 67 Simplifying z = 67
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