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Simplifying (3x + -2y)(3x + 2y) = 0 Multiply (3x + -2y) * (3x + 2y) (3x * (3x + 2y) + -2y * (3x + 2y)) = 0 ((3x * 3x + 2y * 3x) + -2y * (3x + 2y)) = 0 Reorder the terms: ((6xy + 9x2) + -2y * (3x + 2y)) = 0 ((6xy + 9x2) + -2y * (3x + 2y)) = 0 (6xy + 9x2 + (3x * -2y + 2y * -2y)) = 0 (6xy + 9x2 + (-6xy + -4y2)) = 0 Reorder the terms: (6xy + -6xy + 9x2 + -4y2) = 0 Combine like terms: 6xy + -6xy = 0 (0 + 9x2 + -4y2) = 0 (9x2 + -4y2) = 0 Solving 9x2 + -4y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4y2' to each side of the equation. 9x2 + -4y2 + 4y2 = 0 + 4y2 Combine like terms: -4y2 + 4y2 = 0 9x2 + 0 = 0 + 4y2 9x2 = 0 + 4y2 Remove the zero: 9x2 = 4y2 Divide each side by '9'. x2 = 0.4444444444y2 Simplifying x2 = 0.4444444444y2 Take the square root of each side: x = {-0.666666667y, 0.666666667y}
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