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Simplifying
(6x + 7y)(6x + -7y) = 0
Multiply (6x + 7y) * (6x + -7y)
(6x * (6x + -7y) + 7y * (6x + -7y)) = 0
((6x * 6x + -7y * 6x) + 7y * (6x + -7y)) = 0
Reorder the terms:
((-42xy + 36x2) + 7y * (6x + -7y)) = 0
((-42xy + 36x2) + 7y * (6x + -7y)) = 0
(-42xy + 36x2 + (6x * 7y + -7y * 7y)) = 0
(-42xy + 36x2 + (42xy + -49y2)) = 0
Reorder the terms:
(-42xy + 42xy + 36x2 + -49y2) = 0
Combine like terms: -42xy + 42xy = 0
(0 + 36x2 + -49y2) = 0
(36x2 + -49y2) = 0
Solving
36x2 + -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.
36x2 + -49y2 + 49y2 = 0 + 49y2
Combine like terms: -49y2 + 49y2 = 0
36x2 + 0 = 0 + 49y2
36x2 = 0 + 49y2
Remove the zero:
36x2 = 49y2
Divide each side by '36'.
x2 = 1.361111111y2
Simplifying
x2 = 1.361111111y2
Take the square root of each side:
x = {-1.166666667y, 1.166666667y}
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