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Simplifying
(3x + -7y)(3x + 7y) = 0
Multiply (3x + -7y) * (3x + 7y)
(3x * (3x + 7y) + -7y * (3x + 7y)) = 0
((3x * 3x + 7y * 3x) + -7y * (3x + 7y)) = 0
Reorder the terms:
((21xy + 9x2) + -7y * (3x + 7y)) = 0
((21xy + 9x2) + -7y * (3x + 7y)) = 0
(21xy + 9x2 + (3x * -7y + 7y * -7y)) = 0
(21xy + 9x2 + (-21xy + -49y2)) = 0
Reorder the terms:
(21xy + -21xy + 9x2 + -49y2) = 0
Combine like terms: 21xy + -21xy = 0
(0 + 9x2 + -49y2) = 0
(9x2 + -49y2) = 0
Solving
9x2 + -49y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '49y2' to each side of the equation.
9x2 + -49y2 + 49y2 = 0 + 49y2
Combine like terms: -49y2 + 49y2 = 0
9x2 + 0 = 0 + 49y2
9x2 = 0 + 49y2
Remove the zero:
9x2 = 49y2
Divide each side by '9'.
x2 = 5.444444444y2
Simplifying
x2 = 5.444444444y2
Take the square root of each side:
x = {-2.333333333y, 2.333333333y}
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