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Simplifying 8z2 + xc + 32 = (4z + 5)(2z + 7) Reorder the terms: 32 + cx + 8z2 = (4z + 5)(2z + 7) Reorder the terms: 32 + cx + 8z2 = (5 + 4z)(2z + 7) Reorder the terms: 32 + cx + 8z2 = (5 + 4z)(7 + 2z) Multiply (5 + 4z) * (7 + 2z) 32 + cx + 8z2 = (5(7 + 2z) + 4z * (7 + 2z)) 32 + cx + 8z2 = ((7 * 5 + 2z * 5) + 4z * (7 + 2z)) 32 + cx + 8z2 = ((35 + 10z) + 4z * (7 + 2z)) 32 + cx + 8z2 = (35 + 10z + (7 * 4z + 2z * 4z)) 32 + cx + 8z2 = (35 + 10z + (28z + 8z2)) Combine like terms: 10z + 28z = 38z 32 + cx + 8z2 = (35 + 38z + 8z2) Add '-8z2' to each side of the equation. 32 + cx + 8z2 + -8z2 = 35 + 38z + 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 32 + cx + 0 = 35 + 38z + 8z2 + -8z2 32 + cx = 35 + 38z + 8z2 + -8z2 Combine like terms: 8z2 + -8z2 = 0 32 + cx = 35 + 38z + 0 32 + cx = 35 + 38z Solving 32 + cx = 35 + 38z Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + cx = 35 + -32 + 38z Combine like terms: 32 + -32 = 0 0 + cx = 35 + -32 + 38z cx = 35 + -32 + 38z Combine like terms: 35 + -32 = 3 cx = 3 + 38z Divide each side by 'x'. c = 3x-1 + 38x-1z Simplifying c = 3x-1 + 38x-1z
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