x(2x+54)=xy-x

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Solution for x(2x+54)=xy-x equation: 


Simplifying
x(2x + 54) = xy + -1x

Reorder the terms:
x(54 + 2x) = xy + -1x
(54 * x + 2x * x) = xy + -1x
(54x + 2x2) = xy + -1x

Reorder the terms:
54x + 2x2 = -1x + xy

Solving
54x + 2x2 = -1x + xy

Solving for variable 'x'.

Reorder the terms:
54x + x + -1xy + 2x2 = -1x + xy + x + -1xy

Combine like terms: 54x + x = 55x
55x + -1xy + 2x2 = -1x + xy + x + -1xy

Reorder the terms:
55x + -1xy + 2x2 = -1x + x + xy + -1xy

Combine like terms: -1x + x = 0
55x + -1xy + 2x2 = 0 + xy + -1xy
55x + -1xy + 2x2 = xy + -1xy

Combine like terms: xy + -1xy = 0
55x + -1xy + 2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(55 + -1y + 2x) = 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 '(55 + -1y + 2x)' equal to zero and attempt to solve:

Simplifying
55 + -1y + 2x = 0

Reorder the terms:
55 + 2x + -1y = 0

Solving
55 + 2x + -1y = 0

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

Add '-55' to each side of the equation.
55 + 2x + -55 + -1y = 0 + -55

Reorder the terms:
55 + -55 + 2x + -1y = 0 + -55

Combine like terms: 55 + -55 = 0
0 + 2x + -1y = 0 + -55
2x + -1y = 0 + -55

Combine like terms: 0 + -55 = -55
2x + -1y = -55

Add 'y' to each side of the equation.
2x + -1y + y = -55 + y

Combine like terms: -1y + y = 0
2x + 0 = -55 + y
2x = -55 + y

Divide each side by '2'.
x = -27.5 + 0.5y

Simplifying
x = -27.5 + 0.5y
Solution
x = {0, -27.5 + 0.5y}

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