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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 = -39 -39 + -19z + 24z = 4(z + -5) + 12 Combine like terms: -19z + 24z = 5z -39 + 5z = 4(z + -5) + 12 Reorder the terms: -39 + 5z = 4(-5 + z) + 12 -39 + 5z = (-5 * 4 + z * 4) + 12 -39 + 5z = (-20 + 4z) + 12 Reorder the terms: -39 + 5z = -20 + 12 + 4z Combine like terms: -20 + 12 = -8 -39 + 5z = -8 + 4z Solving -39 + 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. -39 + 5z + -4z = -8 + 4z + -4z Combine like terms: 5z + -4z = 1z -39 + 1z = -8 + 4z + -4z Combine like terms: 4z + -4z = 0 -39 + 1z = -8 + 0 -39 + 1z = -8 Add '39' to each side of the equation. -39 + 39 + 1z = -8 + 39 Combine like terms: -39 + 39 = 0 0 + 1z = -8 + 39 1z = -8 + 39 Combine like terms: -8 + 39 = 31 1z = 31 Divide each side by '1'. z = 31 Simplifying z = 31
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