(2y-9)x(2y-9)=x

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Solution for (2y-9)x(2y-9)=x equation: 


Simplifying
(2y + -9) * x(2y + -9) = x

Reorder the terms:
(-9 + 2y) * x(2y + -9) = x

Reorder the terms:
(-9 + 2y) * x(-9 + 2y) = x

Reorder the terms for easier multiplication:
x(-9 + 2y)(-9 + 2y) = x

Multiply (-9 + 2y) * (-9 + 2y)
x(-9(-9 + 2y) + 2y * (-9 + 2y)) = x
x((-9 * -9 + 2y * -9) + 2y * (-9 + 2y)) = x
x((81 + -18y) + 2y * (-9 + 2y)) = x
x(81 + -18y + (-9 * 2y + 2y * 2y)) = x
x(81 + -18y + (-18y + 4y2)) = x

Combine like terms: -18y + -18y = -36y
x(81 + -36y + 4y2) = x
(81 * x + -36y * x + 4y2 * x) = x
(81x + -36xy + 4xy2) = x

Solving
81x + -36xy + 4xy2 = x

Solving for variable 'x'.

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

Add '-1x' to each side of the equation.
81x + -36xy + -1x + 4xy2 = x + -1x

Reorder the terms:
81x + -1x + -36xy + 4xy2 = x + -1x

Combine like terms: 81x + -1x = 80x
80x + -36xy + 4xy2 = x + -1x

Combine like terms: x + -1x = 0
80x + -36xy + 4xy2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(20 + -9y + y2) = 0

Factor a trinomial.
4x((4 + -1y)(5 + -1y)) = 0

Ignore the factor 4.

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 '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Add 'y' to each side of the equation.
-1y + y = -4 + y

Combine like terms: -1y + y = 0
0 = -4 + y

Simplifying
0 = -4 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Add 'y' to each side of the equation.
-1y + y = -5 + y

Combine like terms: -1y + y = 0
0 = -5 + y

Simplifying
0 = -5 + y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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