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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 = 7xy (7xy + 3x2 + 2y2) = 0 Solving 7xy + 3x2 + 2y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + y)(x + 2y) = 0Subproblem 1
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 = -0.3333333333ySubproblem 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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