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Simplifying
(3x + -4y)(3x + 4y) = 0
Multiply (3x + -4y) * (3x + 4y)
(3x * (3x + 4y) + -4y * (3x + 4y)) = 0
((3x * 3x + 4y * 3x) + -4y * (3x + 4y)) = 0
Reorder the terms:
((12xy + 9x2) + -4y * (3x + 4y)) = 0
((12xy + 9x2) + -4y * (3x + 4y)) = 0
(12xy + 9x2 + (3x * -4y + 4y * -4y)) = 0
(12xy + 9x2 + (-12xy + -16y2)) = 0
Reorder the terms:
(12xy + -12xy + 9x2 + -16y2) = 0
Combine like terms: 12xy + -12xy = 0
(0 + 9x2 + -16y2) = 0
(9x2 + -16y2) = 0
Solving
9x2 + -16y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '16y2' to each side of the equation.
9x2 + -16y2 + 16y2 = 0 + 16y2
Combine like terms: -16y2 + 16y2 = 0
9x2 + 0 = 0 + 16y2
9x2 = 0 + 16y2
Remove the zero:
9x2 = 16y2
Divide each side by '9'.
x2 = 1.777777778y2
Simplifying
x2 = 1.777777778y2
Take the square root of each side:
x = {-1.333333333y, 1.333333333y}
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