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Simplifying 8z2 + cz + 34 = (4z + 5)(2z + 7) Reorder the terms: 34 + cz + 8z2 = (4z + 5)(2z + 7) Reorder the terms: 34 + cz + 8z2 = (5 + 4z)(2z + 7) Reorder the terms: 34 + cz + 8z2 = (5 + 4z)(7 + 2z) Multiply (5 + 4z) * (7 + 2z) 34 + cz + 8z2 = (5(7 + 2z) + 4z * (7 + 2z)) 34 + cz + 8z2 = ((7 * 5 + 2z * 5) + 4z * (7 + 2z)) 34 + cz + 8z2 = ((35 + 10z) + 4z * (7 + 2z)) 34 + cz + 8z2 = (35 + 10z + (7 * 4z + 2z * 4z)) 34 + cz + 8z2 = (35 + 10z + (28z + 8z2)) Combine like terms: 10z + 28z = 38z 34 + cz + 8z2 = (35 + 38z + 8z2) Add '-8z2' to each side of the equation. 34 + cz + 8z2 + -8z2 = 35 + 38z + 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 34 + cz + 0 = 35 + 38z + 8z2 + -8z2 34 + cz = 35 + 38z + 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 34 + cz = 35 + 38z + 0 34 + cz = 35 + 38z Solving 34 + cz = 35 + 38z Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + cz = 35 + -34 + 38z Combine like terms: 34 + -34 = 0 0 + cz = 35 + -34 + 38z cz = 35 + -34 + 38z Combine like terms: 35 + -34 = 1 cz = 1 + 38z Divide each side by 'z'. c = z-1 + 38 Simplifying c = z-1 + 38 Reorder the terms: c = 38 + z-1
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