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Simplifying 8(2 + -1z) + 2(5z + -4 + a) = 0 (2 * 8 + -1z * 8) + 2(5z + -4 + a) = 0 (16 + -8z) + 2(5z + -4 + a) = 0 Reorder the terms: 16 + -8z + 2(-4 + a + 5z) = 0 16 + -8z + (-4 * 2 + a * 2 + 5z * 2) = 0 16 + -8z + (-8 + 2a + 10z) = 0 Reorder the terms: 16 + -8 + 2a + -8z + 10z = 0 Combine like terms: 16 + -8 = 8 8 + 2a + -8z + 10z = 0 Combine like terms: -8z + 10z = 2z 8 + 2a + 2z = 0 Solving 8 + 2a + 2z = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + 2a + -8 + 2z = 0 + -8 Reorder the terms: 8 + -8 + 2a + 2z = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 2a + 2z = 0 + -8 2a + 2z = 0 + -8 Combine like terms: 0 + -8 = -8 2a + 2z = -8 Add '-2z' to each side of the equation. 2a + 2z + -2z = -8 + -2z Combine like terms: 2z + -2z = 0 2a + 0 = -8 + -2z 2a = -8 + -2z Divide each side by '2'. a = -4 + -1z Simplifying a = -4 + -1z
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