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Simplifying
(2x + -1y)(2x + y) = 0
Multiply (2x + -1y) * (2x + y)
(2x * (2x + y) + -1y * (2x + y)) = 0
((2x * 2x + y * 2x) + -1y * (2x + y)) = 0
Reorder the terms:
((2xy + 4x2) + -1y * (2x + y)) = 0
((2xy + 4x2) + -1y * (2x + y)) = 0
(2xy + 4x2 + (2x * -1y + y * -1y)) = 0
(2xy + 4x2 + (-2xy + -1y2)) = 0
Reorder the terms:
(2xy + -2xy + 4x2 + -1y2) = 0
Combine like terms: 2xy + -2xy = 0
(0 + 4x2 + -1y2) = 0
(4x2 + -1y2) = 0
Solving
4x2 + -1y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add 'y2' to each side of the equation.
4x2 + -1y2 + y2 = 0 + y2
Combine like terms: -1y2 + y2 = 0
4x2 + 0 = 0 + y2
4x2 = 0 + y2
Remove the zero:
4x2 = y2
Divide each side by '4'.
x2 = 0.25y2
Simplifying
x2 = 0.25y2
Take the square root of each side:
x = {-0.5y, 0.5y}
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