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Simplifying 64z + cz + 34 = (4z + 7)(2z + 5) Reorder the terms: 34 + cz + 64z = (4z + 7)(2z + 5) Reorder the terms: 34 + cz + 64z = (7 + 4z)(2z + 5) Reorder the terms: 34 + cz + 64z = (7 + 4z)(5 + 2z) Multiply (7 + 4z) * (5 + 2z) 34 + cz + 64z = (7(5 + 2z) + 4z * (5 + 2z)) 34 + cz + 64z = ((5 * 7 + 2z * 7) + 4z * (5 + 2z)) 34 + cz + 64z = ((35 + 14z) + 4z * (5 + 2z)) 34 + cz + 64z = (35 + 14z + (5 * 4z + 2z * 4z)) 34 + cz + 64z = (35 + 14z + (20z + 8z2)) Combine like terms: 14z + 20z = 34z 34 + cz + 64z = (35 + 34z + 8z2) Solving 34 + cz + 64z = 35 + 34z + 8z2 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 + cz + -34 + 64z = 35 + 34z + -34 + 8z2 Reorder the terms: 34 + -34 + cz + 64z = 35 + 34z + -34 + 8z2 Combine like terms: 34 + -34 = 0 0 + cz + 64z = 35 + 34z + -34 + 8z2 cz + 64z = 35 + 34z + -34 + 8z2 Reorder the terms: cz + 64z = 35 + -34 + 34z + 8z2 Combine like terms: 35 + -34 = 1 cz + 64z = 1 + 34z + 8z2 Add '-64z' to each side of the equation. cz + 64z + -64z = 1 + 34z + -64z + 8z2 Combine like terms: 64z + -64z = 0 cz + 0 = 1 + 34z + -64z + 8z2 cz = 1 + 34z + -64z + 8z2 Combine like terms: 34z + -64z = -30z cz = 1 + -30z + 8z2 Divide each side by 'z'. c = z-1 + -30 + 8z Simplifying c = z-1 + -30 + 8z Reorder the terms: c = -30 + z-1 + 8z
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