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Simplifying -6(z + 2) + 3(4z + -6) = 5(z + -5) + 13 Reorder the terms: -6(2 + z) + 3(4z + -6) = 5(z + -5) + 13 (2 * -6 + z * -6) + 3(4z + -6) = 5(z + -5) + 13 (-12 + -6z) + 3(4z + -6) = 5(z + -5) + 13 Reorder the terms: -12 + -6z + 3(-6 + 4z) = 5(z + -5) + 13 -12 + -6z + (-6 * 3 + 4z * 3) = 5(z + -5) + 13 -12 + -6z + (-18 + 12z) = 5(z + -5) + 13 Reorder the terms: -12 + -18 + -6z + 12z = 5(z + -5) + 13 Combine like terms: -12 + -18 = -30 -30 + -6z + 12z = 5(z + -5) + 13 Combine like terms: -6z + 12z = 6z -30 + 6z = 5(z + -5) + 13 Reorder the terms: -30 + 6z = 5(-5 + z) + 13 -30 + 6z = (-5 * 5 + z * 5) + 13 -30 + 6z = (-25 + 5z) + 13 Reorder the terms: -30 + 6z = -25 + 13 + 5z Combine like terms: -25 + 13 = -12 -30 + 6z = -12 + 5z Solving -30 + 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. -30 + 6z + -5z = -12 + 5z + -5z Combine like terms: 6z + -5z = 1z -30 + 1z = -12 + 5z + -5z Combine like terms: 5z + -5z = 0 -30 + 1z = -12 + 0 -30 + 1z = -12 Add '30' to each side of the equation. -30 + 30 + 1z = -12 + 30 Combine like terms: -30 + 30 = 0 0 + 1z = -12 + 30 1z = -12 + 30 Combine like terms: -12 + 30 = 18 1z = 18 Divide each side by '1'. z = 18 Simplifying z = 18
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