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Simplifying (x + -1y)(3x + y) = 0 Multiply (x + -1y) * (3x + y) (x(3x + y) + -1y * (3x + y)) = 0 ((3x * x + y * x) + -1y * (3x + y)) = 0 Reorder the terms: ((xy + 3x2) + -1y * (3x + y)) = 0 ((xy + 3x2) + -1y * (3x + y)) = 0 (xy + 3x2 + (3x * -1y + y * -1y)) = 0 (xy + 3x2 + (-3xy + -1y2)) = 0 Reorder the terms: (xy + -3xy + 3x2 + -1y2) = 0 Combine like terms: xy + -3xy = -2xy (-2xy + 3x2 + -1y2) = 0 Solving -2xy + 3x2 + -1y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -1y)(3x + y) = 0Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySolution
x = {y, -0.3333333333y}
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