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Simplifying -5(z + 3) + 4(3z + -4) = 6(z + -3) + 14 Reorder the terms: -5(3 + z) + 4(3z + -4) = 6(z + -3) + 14 (3 * -5 + z * -5) + 4(3z + -4) = 6(z + -3) + 14 (-15 + -5z) + 4(3z + -4) = 6(z + -3) + 14 Reorder the terms: -15 + -5z + 4(-4 + 3z) = 6(z + -3) + 14 -15 + -5z + (-4 * 4 + 3z * 4) = 6(z + -3) + 14 -15 + -5z + (-16 + 12z) = 6(z + -3) + 14 Reorder the terms: -15 + -16 + -5z + 12z = 6(z + -3) + 14 Combine like terms: -15 + -16 = -31 -31 + -5z + 12z = 6(z + -3) + 14 Combine like terms: -5z + 12z = 7z -31 + 7z = 6(z + -3) + 14 Reorder the terms: -31 + 7z = 6(-3 + z) + 14 -31 + 7z = (-3 * 6 + z * 6) + 14 -31 + 7z = (-18 + 6z) + 14 Reorder the terms: -31 + 7z = -18 + 14 + 6z Combine like terms: -18 + 14 = -4 -31 + 7z = -4 + 6z Solving -31 + 7z = -4 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -31 + 7z + -6z = -4 + 6z + -6z Combine like terms: 7z + -6z = 1z -31 + 1z = -4 + 6z + -6z Combine like terms: 6z + -6z = 0 -31 + 1z = -4 + 0 -31 + 1z = -4 Add '31' to each side of the equation. -31 + 31 + 1z = -4 + 31 Combine like terms: -31 + 31 = 0 0 + 1z = -4 + 31 1z = -4 + 31 Combine like terms: -4 + 31 = 27 1z = 27 Divide each side by '1'. z = 27 Simplifying z = 27
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