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Simplifying (3x + y)(x + -2y) = 0 Multiply (3x + y) * (x + -2y) (3x * (x + -2y) + y(x + -2y)) = 0 ((x * 3x + -2y * 3x) + y(x + -2y)) = 0 Reorder the terms: ((-6xy + 3x2) + y(x + -2y)) = 0 ((-6xy + 3x2) + y(x + -2y)) = 0 (-6xy + 3x2 + (x * y + -2y * y)) = 0 (-6xy + 3x2 + (xy + -2y2)) = 0 Reorder the terms: (-6xy + xy + 3x2 + -2y2) = 0 Combine like terms: -6xy + xy = -5xy (-5xy + 3x2 + -2y2) = 0 Solving -5xy + 3x2 + -2y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -2y)(3x + y) = 0Subproblem 1
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySubproblem 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 = {2y, -0.3333333333y}
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