(2x+7y)(2x-7y)+(x-3y)(x+3y)=

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Solution for (2x+7y)(2x-7y)+(x-3y)(x+3y)= equation: 


Simplifying
(2x + 7y)(2x + -7y) + (x + -3y)(x + 3y) = 0

Multiply (2x + 7y) * (2x + -7y)
(2x * (2x + -7y) + 7y * (2x + -7y)) + (x + -3y)(x + 3y) = 0
((2x * 2x + -7y * 2x) + 7y * (2x + -7y)) + (x + -3y)(x + 3y) = 0

Reorder the terms:
((-14xy + 4x2) + 7y * (2x + -7y)) + (x + -3y)(x + 3y) = 0
((-14xy + 4x2) + 7y * (2x + -7y)) + (x + -3y)(x + 3y) = 0
(-14xy + 4x2 + (2x * 7y + -7y * 7y)) + (x + -3y)(x + 3y) = 0
(-14xy + 4x2 + (14xy + -49y2)) + (x + -3y)(x + 3y) = 0

Reorder the terms:
(-14xy + 14xy + 4x2 + -49y2) + (x + -3y)(x + 3y) = 0

Combine like terms: -14xy + 14xy = 0
(0 + 4x2 + -49y2) + (x + -3y)(x + 3y) = 0
(4x2 + -49y2) + (x + -3y)(x + 3y) = 0

Multiply (x + -3y) * (x + 3y)
4x2 + -49y2 + (x(x + 3y) + -3y * (x + 3y)) = 0
4x2 + -49y2 + ((x * x + 3y * x) + -3y * (x + 3y)) = 0

Reorder the terms:
4x2 + -49y2 + ((3xy + x2) + -3y * (x + 3y)) = 0
4x2 + -49y2 + ((3xy + x2) + -3y * (x + 3y)) = 0
4x2 + -49y2 + (3xy + x2 + (x * -3y + 3y * -3y)) = 0
4x2 + -49y2 + (3xy + x2 + (-3xy + -9y2)) = 0

Reorder the terms:
4x2 + -49y2 + (3xy + -3xy + x2 + -9y2) = 0

Combine like terms: 3xy + -3xy = 0
4x2 + -49y2 + (0 + x2 + -9y2) = 0
4x2 + -49y2 + (x2 + -9y2) = 0

Reorder the terms:
4x2 + x2 + -49y2 + -9y2 = 0

Combine like terms: 4x2 + x2 = 5x2
5x2 + -49y2 + -9y2 = 0

Combine like terms: -49y2 + -9y2 = -58y2
5x2 + -58y2 = 0

Solving
5x2 + -58y2 = 0

Solving for variable 'x'.

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

Add '58y2' to each side of the equation.
5x2 + -58y2 + 58y2 = 0 + 58y2

Combine like terms: -58y2 + 58y2 = 0
5x2 + 0 = 0 + 58y2
5x2 = 0 + 58y2
Remove the zero:
5x2 = 58y2

Divide each side by '5'.
x2 = 11.6y2

Simplifying
x2 = 11.6y2

Take the square root of each side:
x = {-3.405877273y, 3.405877273y}

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