(7x+3y)(6x+2y)=

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Solution for (7x+3y)(6x+2y)= equation: 


Simplifying
(7x + 3y)(6x + 2y) = 0

Multiply (7x + 3y) * (6x + 2y)
(7x * (6x + 2y) + 3y * (6x + 2y)) = 0
((6x * 7x + 2y * 7x) + 3y * (6x + 2y)) = 0

Reorder the terms:
((14xy + 42x2) + 3y * (6x + 2y)) = 0
((14xy + 42x2) + 3y * (6x + 2y)) = 0
(14xy + 42x2 + (6x * 3y + 2y * 3y)) = 0
(14xy + 42x2 + (18xy + 6y2)) = 0

Reorder the terms:
(14xy + 18xy + 42x2 + 6y2) = 0

Combine like terms: 14xy + 18xy = 32xy
(32xy + 42x2 + 6y2) = 0

Solving
32xy + 42x2 + 6y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16xy + 21x2 + 3y2) = 0

Factor a trinomial.
2((3x + y)(7x + 3y)) = 0

Ignore the factor 2.

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

Simplifying
3x + y = 0

Solving
3x + y = 0

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

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

Combine like terms: y + -1y = 0
3x + 0 = 0 + -1y
3x = 0 + -1y
Remove the zero:
3x = -1y

Divide each side by '3'.
x = -0.3333333333y

Simplifying
x = -0.3333333333y

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 = {-0.3333333333y, -0.4285714286y}

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