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Simplifying (Z + -17)(2z + 2) = 180 Reorder the terms: (-17 + Z)(2z + 2) = 180 Reorder the terms: (-17 + Z)(2 + 2z) = 180 Multiply (-17 + Z) * (2 + 2z) (-17(2 + 2z) + Z(2 + 2z)) = 180 ((2 * -17 + 2z * -17) + Z(2 + 2z)) = 180 ((-34 + -34z) + Z(2 + 2z)) = 180 (-34 + -34z + (2 * Z + 2z * Z)) = 180 (-34 + -34z + (2Z + 2zZ)) = 180 Reorder the terms: (-34 + 2Z + -34z + 2zZ) = 180 (-34 + 2Z + -34z + 2zZ) = 180 Solving -34 + 2Z + -34z + 2zZ = 180 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '34' to each side of the equation. -34 + 2Z + -34z + 34 + 2zZ = 180 + 34 Reorder the terms: -34 + 34 + 2Z + -34z + 2zZ = 180 + 34 Combine like terms: -34 + 34 = 0 0 + 2Z + -34z + 2zZ = 180 + 34 2Z + -34z + 2zZ = 180 + 34 Combine like terms: 180 + 34 = 214 2Z + -34z + 2zZ = 214 Add '34z' to each side of the equation. 2Z + -34z + 34z + 2zZ = 214 + 34z Combine like terms: -34z + 34z = 0 2Z + 0 + 2zZ = 214 + 34z 2Z + 2zZ = 214 + 34z Reorder the terms: -214 + 2Z + -34z + 2zZ = 214 + 34z + -214 + -34z Reorder the terms: -214 + 2Z + -34z + 2zZ = 214 + -214 + 34z + -34z Combine like terms: 214 + -214 = 0 -214 + 2Z + -34z + 2zZ = 0 + 34z + -34z -214 + 2Z + -34z + 2zZ = 34z + -34z Combine like terms: 34z + -34z = 0 -214 + 2Z + -34z + 2zZ = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-107 + Z + -17z + zZ) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-107 + Z + -17z + zZ)' equal to zero and attempt to solve: Simplifying -107 + Z + -17z + zZ = 0 Solving -107 + Z + -17z + zZ = 0 Move all terms containing Z to the left, all other terms to the right. Add '107' to each side of the equation. -107 + Z + -17z + 107 + zZ = 0 + 107 Reorder the terms: -107 + 107 + Z + -17z + zZ = 0 + 107 Combine like terms: -107 + 107 = 0 0 + Z + -17z + zZ = 0 + 107 Z + -17z + zZ = 0 + 107 Combine like terms: 0 + 107 = 107 Z + -17z + zZ = 107 Add '17z' to each side of the equation. Z + -17z + 17z + zZ = 107 + 17z Combine like terms: -17z + 17z = 0 Z + 0 + zZ = 107 + 17z Z + zZ = 107 + 17z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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