(5x-2y)(6x-3y)=

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Solution for (5x-2y)(6x-3y)= equation: 


Simplifying
(5x + -2y)(6x + -3y) = 0

Multiply (5x + -2y) * (6x + -3y)
(5x * (6x + -3y) + -2y * (6x + -3y)) = 0
((6x * 5x + -3y * 5x) + -2y * (6x + -3y)) = 0

Reorder the terms:
((-15xy + 30x2) + -2y * (6x + -3y)) = 0
((-15xy + 30x2) + -2y * (6x + -3y)) = 0
(-15xy + 30x2 + (6x * -2y + -3y * -2y)) = 0
(-15xy + 30x2 + (-12xy + 6y2)) = 0

Reorder the terms:
(-15xy + -12xy + 30x2 + 6y2) = 0

Combine like terms: -15xy + -12xy = -27xy
(-27xy + 30x2 + 6y2) = 0

Solving
-27xy + 30x2 + 6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9xy + 10x2 + 2y2) = 0

Factor a trinomial.
3((2x + -1y)(5x + -2y)) = 0

Ignore the factor 3.

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

Simplifying
2x + -1y = 0

Solving
2x + -1y = 0

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

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

Combine like terms: -1y + y = 0
2x + 0 = 0 + y
2x = 0 + y
Remove the zero:
2x = y

Divide each side by '2'.
x = 0.5y

Simplifying
x = 0.5y

Subproblem 2
Set the factor '(5x + -2y)' equal to zero and attempt to solve:

Simplifying
5x + -2y = 0

Solving
5x + -2y = 0

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

Add '2y' to each side of the equation.
5x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
5x + 0 = 0 + 2y
5x = 0 + 2y
Remove the zero:
5x = 2y

Divide each side by '5'.
x = 0.4y

Simplifying
x = 0.4y
Solution
x = {0.5y, 0.4y}

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