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Simplifying
(4x + -3y)(4x + 3y) = 0
Multiply (4x + -3y) * (4x + 3y)
(4x * (4x + 3y) + -3y * (4x + 3y)) = 0
((4x * 4x + 3y * 4x) + -3y * (4x + 3y)) = 0
Reorder the terms:
((12xy + 16x2) + -3y * (4x + 3y)) = 0
((12xy + 16x2) + -3y * (4x + 3y)) = 0
(12xy + 16x2 + (4x * -3y + 3y * -3y)) = 0
(12xy + 16x2 + (-12xy + -9y2)) = 0
Reorder the terms:
(12xy + -12xy + 16x2 + -9y2) = 0
Combine like terms: 12xy + -12xy = 0
(0 + 16x2 + -9y2) = 0
(16x2 + -9y2) = 0
Solving
16x2 + -9y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9y2' to each side of the equation.
16x2 + -9y2 + 9y2 = 0 + 9y2
Combine like terms: -9y2 + 9y2 = 0
16x2 + 0 = 0 + 9y2
16x2 = 0 + 9y2
Remove the zero:
16x2 = 9y2
Divide each side by '16'.
x2 = 0.5625y2
Simplifying
x2 = 0.5625y2
Take the square root of each side:
x = {-0.75y, 0.75y}
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