(4+Z)(2+Z)=(4-Z)(2-Z)+8

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Solution for (4+Z)(2+Z)=(4-Z)(2-Z)+8 equation:


Simplifying
(4 + Z)(2 + Z) = (4 + -1Z)(2 + -1Z) + 8

Multiply (4 + Z) * (2 + Z)
(4(2 + Z) + Z(2 + Z)) = (4 + -1Z)(2 + -1Z) + 8
((2 * 4 + Z * 4) + Z(2 + Z)) = (4 + -1Z)(2 + -1Z) + 8
((8 + 4Z) + Z(2 + Z)) = (4 + -1Z)(2 + -1Z) + 8
(8 + 4Z + (2 * Z + Z * Z)) = (4 + -1Z)(2 + -1Z) + 8
(8 + 4Z + (2Z + Z2)) = (4 + -1Z)(2 + -1Z) + 8

Combine like terms: 4Z + 2Z = 6Z
(8 + 6Z + Z2) = (4 + -1Z)(2 + -1Z) + 8

Multiply (4 + -1Z) * (2 + -1Z)
8 + 6Z + Z2 = (4(2 + -1Z) + -1Z * (2 + -1Z)) + 8
8 + 6Z + Z2 = ((2 * 4 + -1Z * 4) + -1Z * (2 + -1Z)) + 8
8 + 6Z + Z2 = ((8 + -4Z) + -1Z * (2 + -1Z)) + 8
8 + 6Z + Z2 = (8 + -4Z + (2 * -1Z + -1Z * -1Z)) + 8
8 + 6Z + Z2 = (8 + -4Z + (-2Z + 1Z2)) + 8

Combine like terms: -4Z + -2Z = -6Z
8 + 6Z + Z2 = (8 + -6Z + 1Z2) + 8

Reorder the terms:
8 + 6Z + Z2 = 8 + 8 + -6Z + 1Z2

Combine like terms: 8 + 8 = 16
8 + 6Z + Z2 = 16 + -6Z + 1Z2

Solving
8 + 6Z + Z2 = 16 + -6Z + 1Z2

Solving for variable 'Z'.

Reorder the terms:
8 + -16 + 6Z + 6Z + Z2 + -1Z2 = 16 + -6Z + 1Z2 + -16 + 6Z + -1Z2

Combine like terms: 8 + -16 = -8
-8 + 6Z + 6Z + Z2 + -1Z2 = 16 + -6Z + 1Z2 + -16 + 6Z + -1Z2

Combine like terms: 6Z + 6Z = 12Z
-8 + 12Z + Z2 + -1Z2 = 16 + -6Z + 1Z2 + -16 + 6Z + -1Z2

Combine like terms: Z2 + -1Z2 = 0
-8 + 12Z + 0 = 16 + -6Z + 1Z2 + -16 + 6Z + -1Z2
-8 + 12Z = 16 + -6Z + 1Z2 + -16 + 6Z + -1Z2

Reorder the terms:
-8 + 12Z = 16 + -16 + -6Z + 6Z + 1Z2 + -1Z2

Combine like terms: 16 + -16 = 0
-8 + 12Z = 0 + -6Z + 6Z + 1Z2 + -1Z2
-8 + 12Z = -6Z + 6Z + 1Z2 + -1Z2

Combine like terms: -6Z + 6Z = 0
-8 + 12Z = 0 + 1Z2 + -1Z2
-8 + 12Z = 1Z2 + -1Z2

Combine like terms: 1Z2 + -1Z2 = 0
-8 + 12Z = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + 3Z) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-2 + 3Z)' equal to zero and attempt to solve: Simplifying -2 + 3Z = 0 Solving -2 + 3Z = 0 Move all terms containing Z to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + 3Z = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 3Z = 0 + 2 3Z = 0 + 2 Combine like terms: 0 + 2 = 2 3Z = 2 Divide each side by '3'. Z = 0.6666666667 Simplifying Z = 0.6666666667

Solution

Z = {0.6666666667}

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