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

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


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

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

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

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

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

Solving
84xy + 42x2 + 42y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '42'.
42(2xy + x2 + y2) = 0

Factor a trinomial.
42((x + y)(x + y)) = 0

Ignore the factor 42.

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y

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

Simplifying
x + y = 0

Solving
x + y = 0

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

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

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

Simplifying
x = -1y
Solution
x = {-1y, -1y}

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