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Simplifying (3y + -1x)(2x + y) = 0 Reorder the terms: (-1x + 3y)(2x + y) = 0 Multiply (-1x + 3y) * (2x + y) (-1x * (2x + y) + 3y * (2x + y)) = 0 ((2x * -1x + y * -1x) + 3y * (2x + y)) = 0 Reorder the terms: ((-1xy + -2x2) + 3y * (2x + y)) = 0 ((-1xy + -2x2) + 3y * (2x + y)) = 0 (-1xy + -2x2 + (2x * 3y + y * 3y)) = 0 (-1xy + -2x2 + (6xy + 3y2)) = 0 Reorder the terms: (-1xy + 6xy + -2x2 + 3y2) = 0 Combine like terms: -1xy + 6xy = 5xy (5xy + -2x2 + 3y2) = 0 Solving 5xy + -2x2 + 3y2 = 0 Solving for variable 'x'. Factor a trinomial. (-2x + -1y)(x + -3y) = 0Subproblem 1
Set the factor '(-2x + -1y)' equal to zero and attempt to solve: Simplifying -2x + -1y = 0 Solving -2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. -2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 -2x + 0 = 0 + y -2x = 0 + y Remove the zero: -2x = y Divide each side by '-2'. x = -0.5y Simplifying x = -0.5ySubproblem 2
Set the factor '(x + -3y)' equal to zero and attempt to solve: Simplifying x + -3y = 0 Solving x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 x + 0 = 0 + 3y x = 0 + 3y Remove the zero: x = 3y Simplifying x = 3ySolution
x = {-0.5y, 3y}
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