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Simplifying
(5x + 4y)(5x + -4y) = 0
Multiply (5x + 4y) * (5x + -4y)
(5x * (5x + -4y) + 4y * (5x + -4y)) = 0
((5x * 5x + -4y * 5x) + 4y * (5x + -4y)) = 0
Reorder the terms:
((-20xy + 25x2) + 4y * (5x + -4y)) = 0
((-20xy + 25x2) + 4y * (5x + -4y)) = 0
(-20xy + 25x2 + (5x * 4y + -4y * 4y)) = 0
(-20xy + 25x2 + (20xy + -16y2)) = 0
Reorder the terms:
(-20xy + 20xy + 25x2 + -16y2) = 0
Combine like terms: -20xy + 20xy = 0
(0 + 25x2 + -16y2) = 0
(25x2 + -16y2) = 0
Solving
25x2 + -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.
25x2 + -16y2 + 16y2 = 0 + 16y2
Combine like terms: -16y2 + 16y2 = 0
25x2 + 0 = 0 + 16y2
25x2 = 0 + 16y2
Remove the zero:
25x2 = 16y2
Divide each side by '25'.
x2 = 0.64y2
Simplifying
x2 = 0.64y2
Take the square root of each side:
x = {-0.8y, 0.8y}
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