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