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Simplifying
(4x + 7y)(4x + -7y) = 0
Multiply (4x + 7y) * (4x + -7y)
(4x * (4x + -7y) + 7y * (4x + -7y)) = 0
((4x * 4x + -7y * 4x) + 7y * (4x + -7y)) = 0
Reorder the terms:
((-28xy + 16x2) + 7y * (4x + -7y)) = 0
((-28xy + 16x2) + 7y * (4x + -7y)) = 0
(-28xy + 16x2 + (4x * 7y + -7y * 7y)) = 0
(-28xy + 16x2 + (28xy + -49y2)) = 0
Reorder the terms:
(-28xy + 28xy + 16x2 + -49y2) = 0
Combine like terms: -28xy + 28xy = 0
(0 + 16x2 + -49y2) = 0
(16x2 + -49y2) = 0
Solving
16x2 + -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.
16x2 + -49y2 + 49y2 = 0 + 49y2
Combine like terms: -49y2 + 49y2 = 0
16x2 + 0 = 0 + 49y2
16x2 = 0 + 49y2
Remove the zero:
16x2 = 49y2
Divide each side by '16'.
x2 = 3.0625y2
Simplifying
x2 = 3.0625y2
Take the square root of each side:
x = {-1.75y, 1.75y}
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