(2x^2+9xy)(9y-x)=

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


Simplifying
(2x2 + 9xy)(9y + -1x) = 0

Reorder the terms:
(9xy + 2x2)(9y + -1x) = 0

Reorder the terms:
(9xy + 2x2)(-1x + 9y) = 0

Multiply (9xy + 2x2) * (-1x + 9y)
(9xy * (-1x + 9y) + 2x2 * (-1x + 9y)) = 0
((-1x * 9xy + 9y * 9xy) + 2x2 * (-1x + 9y)) = 0

Reorder the terms:
((81xy2 + -9x2y) + 2x2 * (-1x + 9y)) = 0
((81xy2 + -9x2y) + 2x2 * (-1x + 9y)) = 0
(81xy2 + -9x2y + (-1x * 2x2 + 9y * 2x2)) = 0

Reorder the terms:
(81xy2 + -9x2y + (18x2y + -2x3)) = 0
(81xy2 + -9x2y + (18x2y + -2x3)) = 0

Combine like terms: -9x2y + 18x2y = 9x2y
(81xy2 + 9x2y + -2x3) = 0

Solving
81xy2 + 9x2y + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(81y2 + 9xy + -2x2) = 0

Factor a trinomial.
x((9y + -1x)(9y + 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 '(9y + -1x)' equal to zero and attempt to solve:

Simplifying
9y + -1x = 0

Reorder the terms:
-1x + 9y = 0

Solving
-1x + 9y = 0

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

Add '-9y' to each side of the equation.
-1x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
-1x + 0 = 0 + -9y
-1x = 0 + -9y
Remove the zero:
-1x = -9y

Divide each side by '-1'.
x = 9y

Simplifying
x = 9y

Subproblem 3
Set the factor '(9y + 2x)' equal to zero and attempt to solve:

Simplifying
9y + 2x = 0

Reorder the terms:
2x + 9y = 0

Solving
2x + 9y = 0

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

Add '-9y' to each side of the equation.
2x + 9y + -9y = 0 + -9y

Combine like terms: 9y + -9y = 0
2x + 0 = 0 + -9y
2x = 0 + -9y
Remove the zero:
2x = -9y

Divide each side by '2'.
x = -4.5y

Simplifying
x = -4.5y
Solution
x = {0, 9y, -4.5y}

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