=9x(2x+3y-1)

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Solution for =9x(2x+3y-1) equation: 


Simplifying
0 = 9x(2x + 3y + -1)

Reorder the terms:
0 = 9x(-1 + 2x + 3y)
0 = (-1 * 9x + 2x * 9x + 3y * 9x)

Reorder the terms:
0 = (-9x + 27xy + 18x2)
0 = (-9x + 27xy + 18x2)

Solving
0 = -9x + 27xy + 18x2

Solving for variable 'x'.
Remove the zero:
9x + -27xy + -18x2 = -9x + 27xy + 18x2 + 9x + -27xy + -18x2

Reorder the terms:
9x + -27xy + -18x2 = -9x + 9x + 27xy + -27xy + 18x2 + -18x2

Combine like terms: -9x + 9x = 0
9x + -27xy + -18x2 = 0 + 27xy + -27xy + 18x2 + -18x2
9x + -27xy + -18x2 = 27xy + -27xy + 18x2 + -18x2

Combine like terms: 27xy + -27xy = 0
9x + -27xy + -18x2 = 0 + 18x2 + -18x2
9x + -27xy + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
9x + -27xy + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '9x'.
9x(1 + -3y + -2x) = 0

Ignore the factor 9.

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 '(1 + -3y + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -3y + -2x = 0

Reorder the terms:
1 + -2x + -3y = 0

Solving
1 + -2x + -3y = 0

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

Add '-1' to each side of the equation.
1 + -2x + -1 + -3y = 0 + -1

Reorder the terms:
1 + -1 + -2x + -3y = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x + -3y = 0 + -1
-2x + -3y = 0 + -1

Combine like terms: 0 + -1 = -1
-2x + -3y = -1

Add '3y' to each side of the equation.
-2x + -3y + 3y = -1 + 3y

Combine like terms: -3y + 3y = 0
-2x + 0 = -1 + 3y
-2x = -1 + 3y

Divide each side by '-2'.
x = 0.5 + -1.5y

Simplifying
x = 0.5 + -1.5y
Solution
x = {0, 0.5 + -1.5y}

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