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

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


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

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

Reorder the terms:
((6xy + 7x2) + 7y * (7x + 6y)) = 0
((6xy + 7x2) + 7y * (7x + 6y)) = 0
(6xy + 7x2 + (7x * 7y + 6y * 7y)) = 0
(6xy + 7x2 + (49xy + 42y2)) = 0

Reorder the terms:
(6xy + 49xy + 7x2 + 42y2) = 0

Combine like terms: 6xy + 49xy = 55xy
(55xy + 7x2 + 42y2) = 0

Solving
55xy + 7x2 + 42y2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(7x + 6y)' equal to zero and attempt to solve:

Simplifying
7x + 6y = 0

Solving
7x + 6y = 0

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

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

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

Divide each side by '7'.
x = -0.8571428571y

Simplifying
x = -0.8571428571y

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

Simplifying
x + 7y = 0

Solving
x + 7y = 0

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

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

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

Simplifying
x = -7y
Solution
x = {-0.8571428571y, -7y}

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