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Simplifying -2(z + 2) + 3(3z + -4) = 6(z + -3) + 10 Reorder the terms: -2(2 + z) + 3(3z + -4) = 6(z + -3) + 10 (2 * -2 + z * -2) + 3(3z + -4) = 6(z + -3) + 10 (-4 + -2z) + 3(3z + -4) = 6(z + -3) + 10 Reorder the terms: -4 + -2z + 3(-4 + 3z) = 6(z + -3) + 10 -4 + -2z + (-4 * 3 + 3z * 3) = 6(z + -3) + 10 -4 + -2z + (-12 + 9z) = 6(z + -3) + 10 Reorder the terms: -4 + -12 + -2z + 9z = 6(z + -3) + 10 Combine like terms: -4 + -12 = -16 -16 + -2z + 9z = 6(z + -3) + 10 Combine like terms: -2z + 9z = 7z -16 + 7z = 6(z + -3) + 10 Reorder the terms: -16 + 7z = 6(-3 + z) + 10 -16 + 7z = (-3 * 6 + z * 6) + 10 -16 + 7z = (-18 + 6z) + 10 Reorder the terms: -16 + 7z = -18 + 10 + 6z Combine like terms: -18 + 10 = -8 -16 + 7z = -8 + 6z Solving -16 + 7z = -8 + 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. -16 + 7z + -6z = -8 + 6z + -6z Combine like terms: 7z + -6z = 1z -16 + 1z = -8 + 6z + -6z Combine like terms: 6z + -6z = 0 -16 + 1z = -8 + 0 -16 + 1z = -8 Add '16' to each side of the equation. -16 + 16 + 1z = -8 + 16 Combine like terms: -16 + 16 = 0 0 + 1z = -8 + 16 1z = -8 + 16 Combine like terms: -8 + 16 = 8 1z = 8 Divide each side by '1'. z = 8 Simplifying z = 8
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