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Simplifying -1(4z + -4)(2z + 6) = z(13 + -8z) Reorder the terms: -1(-4 + 4z)(2z + 6) = z(13 + -8z) Reorder the terms: -1(-4 + 4z)(6 + 2z) = z(13 + -8z) Multiply (-4 + 4z) * (6 + 2z) -1(-4(6 + 2z) + 4z * (6 + 2z)) = z(13 + -8z) -1((6 * -4 + 2z * -4) + 4z * (6 + 2z)) = z(13 + -8z) -1((-24 + -8z) + 4z * (6 + 2z)) = z(13 + -8z) -1(-24 + -8z + (6 * 4z + 2z * 4z)) = z(13 + -8z) -1(-24 + -8z + (24z + 8z2)) = z(13 + -8z) Combine like terms: -8z + 24z = 16z -1(-24 + 16z + 8z2) = z(13 + -8z) (-24 * -1 + 16z * -1 + 8z2 * -1) = z(13 + -8z) (24 + -16z + -8z2) = z(13 + -8z) 24 + -16z + -8z2 = (13 * z + -8z * z) 24 + -16z + -8z2 = (13z + -8z2) Add '8z2' to each side of the equation. 24 + -16z + -8z2 + 8z2 = 13z + -8z2 + 8z2 Combine like terms: -8z2 + 8z2 = 0 24 + -16z + 0 = 13z + -8z2 + 8z2 24 + -16z = 13z + -8z2 + 8z2 Combine like terms: -8z2 + 8z2 = 0 24 + -16z = 13z + 0 24 + -16z = 13z Solving 24 + -16z = 13z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13z' to each side of the equation. 24 + -16z + -13z = 13z + -13z Combine like terms: -16z + -13z = -29z 24 + -29z = 13z + -13z Combine like terms: 13z + -13z = 0 24 + -29z = 0 Add '-24' to each side of the equation. 24 + -24 + -29z = 0 + -24 Combine like terms: 24 + -24 = 0 0 + -29z = 0 + -24 -29z = 0 + -24 Combine like terms: 0 + -24 = -24 -29z = -24 Divide each side by '-29'. z = 0.8275862069 Simplifying z = 0.8275862069
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