=(9x-2y)(4x-3y)

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Solution for =(9x-2y)(4x-3y) equation: 


Simplifying
0 = (9x + -2y)(4x + -3y)

Multiply (9x + -2y) * (4x + -3y)
0 = (9x * (4x + -3y) + -2y * (4x + -3y))
0 = ((4x * 9x + -3y * 9x) + -2y * (4x + -3y))

Reorder the terms:
0 = ((-27xy + 36x2) + -2y * (4x + -3y))
0 = ((-27xy + 36x2) + -2y * (4x + -3y))
0 = (-27xy + 36x2 + (4x * -2y + -3y * -2y))
0 = (-27xy + 36x2 + (-8xy + 6y2))

Reorder the terms:
0 = (-27xy + -8xy + 36x2 + 6y2)

Combine like terms: -27xy + -8xy = -35xy
0 = (-35xy + 36x2 + 6y2)

Solving
0 = -35xy + 36x2 + 6y2

Solving for variable 'x'.
Remove the zero:
35xy + -36x2 + -6y2 = -35xy + 36x2 + 6y2 + 35xy + -36x2 + -6y2

Reorder the terms:
35xy + -36x2 + -6y2 = -35xy + 35xy + 36x2 + -36x2 + 6y2 + -6y2

Combine like terms: -35xy + 35xy = 0
35xy + -36x2 + -6y2 = 0 + 36x2 + -36x2 + 6y2 + -6y2
35xy + -36x2 + -6y2 = 36x2 + -36x2 + 6y2 + -6y2

Combine like terms: 36x2 + -36x2 = 0
35xy + -36x2 + -6y2 = 0 + 6y2 + -6y2
35xy + -36x2 + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
35xy + -36x2 + -6y2 = 0

Factor a trinomial.
(-9x + 2y)(4x + -3y) = 0


Subproblem 1
Set the factor '(-9x + 2y)' equal to zero and attempt to solve:

Simplifying
-9x + 2y = 0

Solving
-9x + 2y = 0

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

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

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

Divide each side by '-9'.
x = 0.2222222222y

Simplifying
x = 0.2222222222y

Subproblem 2
Set the factor '(4x + -3y)' equal to zero and attempt to solve:

Simplifying
4x + -3y = 0

Solving
4x + -3y = 0

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

Add '3y' to each side of the equation.
4x + -3y + 3y = 0 + 3y

Combine like terms: -3y + 3y = 0
4x + 0 = 0 + 3y
4x = 0 + 3y
Remove the zero:
4x = 3y

Divide each side by '4'.
x = 0.75y

Simplifying
x = 0.75y
Solution
x = {0.2222222222y, 0.75y}

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