(7x+2y)(7x+2y)=0

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Solution for (7x+2y)(7x+2y)=0 equation: 


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

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

Reorder the terms:
((14xy + 49x2) + 2y * (7x + 2y)) = 0
((14xy + 49x2) + 2y * (7x + 2y)) = 0
(14xy + 49x2 + (7x * 2y + 2y * 2y)) = 0
(14xy + 49x2 + (14xy + 4y2)) = 0

Reorder the terms:
(14xy + 14xy + 49x2 + 4y2) = 0

Combine like terms: 14xy + 14xy = 28xy
(28xy + 49x2 + 4y2) = 0

Solving
28xy + 49x2 + 4y2 = 0

Solving for variable 'x'.

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


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

Simplifying
7x + 2y = 0

Solving
7x + 2y = 0

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

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

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

Divide each side by '7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y

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

Simplifying
7x + 2y = 0

Solving
7x + 2y = 0

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

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

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

Divide each side by '7'.
x = -0.2857142857y

Simplifying
x = -0.2857142857y
Solution
x = {-0.2857142857y, -0.2857142857y}

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