(6x+21y)(6x+21y)=

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Solution for (6x+21y)(6x+21y)= equation: 


Simplifying
(6x + 21y)(6x + 21y) = 0

Multiply (6x + 21y) * (6x + 21y)
(6x * (6x + 21y) + 21y * (6x + 21y)) = 0
((6x * 6x + 21y * 6x) + 21y * (6x + 21y)) = 0

Reorder the terms:
((126xy + 36x2) + 21y * (6x + 21y)) = 0
((126xy + 36x2) + 21y * (6x + 21y)) = 0
(126xy + 36x2 + (6x * 21y + 21y * 21y)) = 0
(126xy + 36x2 + (126xy + 441y2)) = 0

Reorder the terms:
(126xy + 126xy + 36x2 + 441y2) = 0

Combine like terms: 126xy + 126xy = 252xy
(252xy + 36x2 + 441y2) = 0

Solving
252xy + 36x2 + 441y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9'.
9(28xy + 4x2 + 49y2) = 0

Factor a trinomial.
9((2x + 7y)(2x + 7y)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(2x + 7y)' equal to zero and attempt to solve:

Simplifying
2x + 7y = 0

Solving
2x + 7y = 0

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

Add '-7y' to each side of the equation.
2x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
2x + 0 = 0 + -7y
2x = 0 + -7y
Remove the zero:
2x = -7y

Divide each side by '2'.
x = -3.5y

Simplifying
x = -3.5y

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

Simplifying
2x + 7y = 0

Solving
2x + 7y = 0

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

Add '-7y' to each side of the equation.
2x + 7y + -7y = 0 + -7y

Combine like terms: 7y + -7y = 0
2x + 0 = 0 + -7y
2x = 0 + -7y
Remove the zero:
2x = -7y

Divide each side by '2'.
x = -3.5y

Simplifying
x = -3.5y
Solution
x = {-3.5y, -3.5y}

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