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Simplifying -6(z + 2) + 3(4z + -3) = 5(z + -3) + 12 Reorder the terms: -6(2 + z) + 3(4z + -3) = 5(z + -3) + 12 (2 * -6 + z * -6) + 3(4z + -3) = 5(z + -3) + 12 (-12 + -6z) + 3(4z + -3) = 5(z + -3) + 12 Reorder the terms: -12 + -6z + 3(-3 + 4z) = 5(z + -3) + 12 -12 + -6z + (-3 * 3 + 4z * 3) = 5(z + -3) + 12 -12 + -6z + (-9 + 12z) = 5(z + -3) + 12 Reorder the terms: -12 + -9 + -6z + 12z = 5(z + -3) + 12 Combine like terms: -12 + -9 = -21 -21 + -6z + 12z = 5(z + -3) + 12 Combine like terms: -6z + 12z = 6z -21 + 6z = 5(z + -3) + 12 Reorder the terms: -21 + 6z = 5(-3 + z) + 12 -21 + 6z = (-3 * 5 + z * 5) + 12 -21 + 6z = (-15 + 5z) + 12 Reorder the terms: -21 + 6z = -15 + 12 + 5z Combine like terms: -15 + 12 = -3 -21 + 6z = -3 + 5z Solving -21 + 6z = -3 + 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. -21 + 6z + -5z = -3 + 5z + -5z Combine like terms: 6z + -5z = 1z -21 + 1z = -3 + 5z + -5z Combine like terms: 5z + -5z = 0 -21 + 1z = -3 + 0 -21 + 1z = -3 Add '21' to each side of the equation. -21 + 21 + 1z = -3 + 21 Combine like terms: -21 + 21 = 0 0 + 1z = -3 + 21 1z = -3 + 21 Combine like terms: -3 + 21 = 18 1z = 18 Divide each side by '1'. z = 18 Simplifying z = 18
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