(3x-5y)(6x-7y)=

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Solution for (3x-5y)(6x-7y)= equation: 


Simplifying
(3x + -5y)(6x + -7y) = 0

Multiply (3x + -5y) * (6x + -7y)
(3x * (6x + -7y) + -5y * (6x + -7y)) = 0
((6x * 3x + -7y * 3x) + -5y * (6x + -7y)) = 0

Reorder the terms:
((-21xy + 18x2) + -5y * (6x + -7y)) = 0
((-21xy + 18x2) + -5y * (6x + -7y)) = 0
(-21xy + 18x2 + (6x * -5y + -7y * -5y)) = 0
(-21xy + 18x2 + (-30xy + 35y2)) = 0

Reorder the terms:
(-21xy + -30xy + 18x2 + 35y2) = 0

Combine like terms: -21xy + -30xy = -51xy
(-51xy + 18x2 + 35y2) = 0

Solving
-51xy + 18x2 + 35y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -5y)(6x + -7y) = 0


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

Simplifying
3x + -5y = 0

Solving
3x + -5y = 0

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

Add '5y' to each side of the equation.
3x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
3x + 0 = 0 + 5y
3x = 0 + 5y
Remove the zero:
3x = 5y

Divide each side by '3'.
x = 1.666666667y

Simplifying
x = 1.666666667y

Subproblem 2
Set the factor '(6x + -7y)' equal to zero and attempt to solve:

Simplifying
6x + -7y = 0

Solving
6x + -7y = 0

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

Add '7y' to each side of the equation.
6x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
6x + 0 = 0 + 7y
6x = 0 + 7y
Remove the zero:
6x = 7y

Divide each side by '6'.
x = 1.166666667y

Simplifying
x = 1.166666667y
Solution
x = {1.666666667y, 1.166666667y}

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