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

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


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

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

Reorder the terms:
((-35xy + 42x2) + 3y * (6x + -5y)) = 0
((-35xy + 42x2) + 3y * (6x + -5y)) = 0
(-35xy + 42x2 + (6x * 3y + -5y * 3y)) = 0
(-35xy + 42x2 + (18xy + -15y2)) = 0

Reorder the terms:
(-35xy + 18xy + 42x2 + -15y2) = 0

Combine like terms: -35xy + 18xy = -17xy
(-17xy + 42x2 + -15y2) = 0

Solving
-17xy + 42x2 + -15y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(6x + -5y)' equal to zero and attempt to solve:

Simplifying
6x + -5y = 0

Solving
6x + -5y = 0

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

Add '5y' to each side of the equation.
6x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
6x + 0 = 0 + 5y
6x = 0 + 5y
Remove the zero:
6x = 5y

Divide each side by '6'.
x = 0.8333333333y

Simplifying
x = 0.8333333333y

Subproblem 2
Set the factor '(7x + 3y)' equal to zero and attempt to solve:

Simplifying
7x + 3y = 0

Solving
7x + 3y = 0

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

Add '-3y' to each side of the equation.
7x + 3y + -3y = 0 + -3y

Combine like terms: 3y + -3y = 0
7x + 0 = 0 + -3y
7x = 0 + -3y
Remove the zero:
7x = -3y

Divide each side by '7'.
x = -0.4285714286y

Simplifying
x = -0.4285714286y
Solution
x = {0.8333333333y, -0.4285714286y}

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