0=(27-x-y)x-3x

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Solution for 0=(27-x-y)x-3x equation: 


Simplifying
0 = (27 + -1x + -1y) * x + -3x

Reorder the terms for easier multiplication:
0 = x(27 + -1x + -1y) + -3x
0 = (27 * x + -1x * x + -1y * x) + -3x

Reorder the terms:
0 = (27x + -1xy + -1x2) + -3x
0 = (27x + -1xy + -1x2) + -3x

Reorder the terms:
0 = 27x + -3x + -1xy + -1x2

Combine like terms: 27x + -3x = 24x
0 = 24x + -1xy + -1x2

Solving
0 = 24x + -1xy + -1x2

Solving for variable 'x'.
Remove the zero:
-24x + xy + x2 = 24x + -1xy + -1x2 + -24x + xy + x2

Reorder the terms:
-24x + xy + x2 = 24x + -24x + -1xy + xy + -1x2 + x2

Combine like terms: 24x + -24x = 0
-24x + xy + x2 = 0 + -1xy + xy + -1x2 + x2
-24x + xy + x2 = -1xy + xy + -1x2 + x2

Combine like terms: -1xy + xy = 0
-24x + xy + x2 = 0 + -1x2 + x2
-24x + xy + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-24x + xy + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + y + x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-24 + y + x)' equal to zero and attempt to solve:

Simplifying
-24 + y + x = 0

Reorder the terms:
-24 + x + y = 0

Solving
-24 + x + y = 0

Move all terms containing x to the left, all other terms to the right.

Add '24' to each side of the equation.
-24 + x + 24 + y = 0 + 24

Reorder the terms:
-24 + 24 + x + y = 0 + 24

Combine like terms: -24 + 24 = 0
0 + x + y = 0 + 24
x + y = 0 + 24

Combine like terms: 0 + 24 = 24
x + y = 24

Add '-1y' to each side of the equation.
x + y + -1y = 24 + -1y

Combine like terms: y + -1y = 0
x + 0 = 24 + -1y
x = 24 + -1y

Simplifying
x = 24 + -1y
Solution
x = {0, 24 + -1y}

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