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Simplifying
(5x + 3y)(5x + -3y) = 0
Multiply (5x + 3y) * (5x + -3y)
(5x * (5x + -3y) + 3y * (5x + -3y)) = 0
((5x * 5x + -3y * 5x) + 3y * (5x + -3y)) = 0
Reorder the terms:
((-15xy + 25x2) + 3y * (5x + -3y)) = 0
((-15xy + 25x2) + 3y * (5x + -3y)) = 0
(-15xy + 25x2 + (5x * 3y + -3y * 3y)) = 0
(-15xy + 25x2 + (15xy + -9y2)) = 0
Reorder the terms:
(-15xy + 15xy + 25x2 + -9y2) = 0
Combine like terms: -15xy + 15xy = 0
(0 + 25x2 + -9y2) = 0
(25x2 + -9y2) = 0
Solving
25x2 + -9y2 = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '9y2' to each side of the equation.
25x2 + -9y2 + 9y2 = 0 + 9y2
Combine like terms: -9y2 + 9y2 = 0
25x2 + 0 = 0 + 9y2
25x2 = 0 + 9y2
Remove the zero:
25x2 = 9y2
Divide each side by '25'.
x2 = 0.36y2
Simplifying
x2 = 0.36y2
Take the square root of each side:
x = {-0.6y, 0.6y}
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