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Simplifying
(7x + -12y)(7x + 12y) = 0
Multiply (7x + -12y) * (7x + 12y)
(7x * (7x + 12y) + -12y * (7x + 12y)) = 0
((7x * 7x + 12y * 7x) + -12y * (7x + 12y)) = 0
Reorder the terms:
((84xy + 49x2) + -12y * (7x + 12y)) = 0
((84xy + 49x2) + -12y * (7x + 12y)) = 0
(84xy + 49x2 + (7x * -12y + 12y * -12y)) = 0
(84xy + 49x2 + (-84xy + -144y2)) = 0
Reorder the terms:
(84xy + -84xy + 49x2 + -144y2) = 0
Combine like terms: 84xy + -84xy = 0
(0 + 49x2 + -144y2) = 0
(49x2 + -144y2) = 0
Solving
49x2 + -144y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '144y2' to each side of the equation.
49x2 + -144y2 + 144y2 = 0 + 144y2
Combine like terms: -144y2 + 144y2 = 0
49x2 + 0 = 0 + 144y2
49x2 = 0 + 144y2
Remove the zero:
49x2 = 144y2
Divide each side by '49'.
x2 = 2.93877551y2
Simplifying
x2 = 2.93877551y2
Take the square root of each side:
x = {-1.714285714y, 1.714285714y}
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