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Simplifying 8(z + -1(3z + 21) + 5) = 4(z + 8) Reorder the terms: 8(z + -1(21 + 3z) + 5) = 4(z + 8) 8(z + (21 * -1 + 3z * -1) + 5) = 4(z + 8) 8(z + (-21 + -3z) + 5) = 4(z + 8) Reorder the terms: 8(-21 + 5 + z + -3z) = 4(z + 8) Combine like terms: -21 + 5 = -16 8(-16 + z + -3z) = 4(z + 8) Combine like terms: z + -3z = -2z 8(-16 + -2z) = 4(z + 8) (-16 * 8 + -2z * 8) = 4(z + 8) (-128 + -16z) = 4(z + 8) Reorder the terms: -128 + -16z = 4(8 + z) -128 + -16z = (8 * 4 + z * 4) -128 + -16z = (32 + 4z) Solving -128 + -16z = 32 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -128 + -16z + -4z = 32 + 4z + -4z Combine like terms: -16z + -4z = -20z -128 + -20z = 32 + 4z + -4z Combine like terms: 4z + -4z = 0 -128 + -20z = 32 + 0 -128 + -20z = 32 Add '128' to each side of the equation. -128 + 128 + -20z = 32 + 128 Combine like terms: -128 + 128 = 0 0 + -20z = 32 + 128 -20z = 32 + 128 Combine like terms: 32 + 128 = 160 -20z = 160 Divide each side by '-20'. z = -8 Simplifying z = -8
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