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

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Solution for (7x+6y)(7x+6y)=0 equation: 


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

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

Reorder the terms:
((42xy + 49x2) + 6y * (7x + 6y)) = 0
((42xy + 49x2) + 6y * (7x + 6y)) = 0
(42xy + 49x2 + (7x * 6y + 6y * 6y)) = 0
(42xy + 49x2 + (42xy + 36y2)) = 0

Reorder the terms:
(42xy + 42xy + 49x2 + 36y2) = 0

Combine like terms: 42xy + 42xy = 84xy
(84xy + 49x2 + 36y2) = 0

Solving
84xy + 49x2 + 36y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7x + 6y)(7x + 6y) = 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 '(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
Solution
x = {-0.8571428571y, -0.8571428571y}

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