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Simplifying
(5x + 10y)(5x + -10y) = 0
Multiply (5x + 10y) * (5x + -10y)
(5x * (5x + -10y) + 10y * (5x + -10y)) = 0
((5x * 5x + -10y * 5x) + 10y * (5x + -10y)) = 0
Reorder the terms:
((-50xy + 25x2) + 10y * (5x + -10y)) = 0
((-50xy + 25x2) + 10y * (5x + -10y)) = 0
(-50xy + 25x2 + (5x * 10y + -10y * 10y)) = 0
(-50xy + 25x2 + (50xy + -100y2)) = 0
Reorder the terms:
(-50xy + 50xy + 25x2 + -100y2) = 0
Combine like terms: -50xy + 50xy = 0
(0 + 25x2 + -100y2) = 0
(25x2 + -100y2) = 0
Solving
25x2 + -100y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '100y2' to each side of the equation.
25x2 + -100y2 + 100y2 = 0 + 100y2
Combine like terms: -100y2 + 100y2 = 0
25x2 + 0 = 0 + 100y2
25x2 = 0 + 100y2
Remove the zero:
25x2 = 100y2
Divide each side by '25'.
x2 = 4y2
Simplifying
x2 = 4y2
Take the square root of each side:
x = {-2y, 2y}
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