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Simplifying
(4ya + -6xb)(4ya + 6xb) = 0
Multiply (4ay + -6bx) * (4ay + 6bx)
(4ay * (4ay + 6bx) + -6bx * (4ay + 6bx)) = 0
((4ay * 4ay + 6bx * 4ay) + -6bx * (4ay + 6bx)) = 0
Reorder the terms:
((24abxy + 16a2y2) + -6bx * (4ay + 6bx)) = 0
((24abxy + 16a2y2) + -6bx * (4ay + 6bx)) = 0
(24abxy + 16a2y2 + (4ay * -6bx + 6bx * -6bx)) = 0
(24abxy + 16a2y2 + (-24abxy + -36b2x2)) = 0
Reorder the terms:
(24abxy + -24abxy + 16a2y2 + -36b2x2) = 0
Combine like terms: 24abxy + -24abxy = 0
(0 + 16a2y2 + -36b2x2) = 0
(16a2y2 + -36b2x2) = 0
Solving
16a2y2 + -36b2x2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '36b2x2' to each side of the equation.
16a2y2 + -36b2x2 + 36b2x2 = 0 + 36b2x2
Combine like terms: -36b2x2 + 36b2x2 = 0
16a2y2 + 0 = 0 + 36b2x2
16a2y2 = 0 + 36b2x2
Remove the zero:
16a2y2 = 36b2x2
Divide each side by '16y2'.
a2 = 2.25b2x2y-2
Simplifying
a2 = 2.25b2x2y-2
Take the square root of each side:
a = {-1.5bxy-1, 1.5bxy-1}
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