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Simplifying -12(z + 1) + 6(3z + -4) = 5(z + -4) + 13 Reorder the terms: -12(1 + z) + 6(3z + -4) = 5(z + -4) + 13 (1 * -12 + z * -12) + 6(3z + -4) = 5(z + -4) + 13 (-12 + -12z) + 6(3z + -4) = 5(z + -4) + 13 Reorder the terms: -12 + -12z + 6(-4 + 3z) = 5(z + -4) + 13 -12 + -12z + (-4 * 6 + 3z * 6) = 5(z + -4) + 13 -12 + -12z + (-24 + 18z) = 5(z + -4) + 13 Reorder the terms: -12 + -24 + -12z + 18z = 5(z + -4) + 13 Combine like terms: -12 + -24 = -36 -36 + -12z + 18z = 5(z + -4) + 13 Combine like terms: -12z + 18z = 6z -36 + 6z = 5(z + -4) + 13 Reorder the terms: -36 + 6z = 5(-4 + z) + 13 -36 + 6z = (-4 * 5 + z * 5) + 13 -36 + 6z = (-20 + 5z) + 13 Reorder the terms: -36 + 6z = -20 + 13 + 5z Combine like terms: -20 + 13 = -7 -36 + 6z = -7 + 5z Solving -36 + 6z = -7 + 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. -36 + 6z + -5z = -7 + 5z + -5z Combine like terms: 6z + -5z = 1z -36 + 1z = -7 + 5z + -5z Combine like terms: 5z + -5z = 0 -36 + 1z = -7 + 0 -36 + 1z = -7 Add '36' to each side of the equation. -36 + 36 + 1z = -7 + 36 Combine like terms: -36 + 36 = 0 0 + 1z = -7 + 36 1z = -7 + 36 Combine like terms: -7 + 36 = 29 1z = 29 Divide each side by '1'. z = 29 Simplifying z = 29
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