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Simplifying (x + 5y)(3x + 2y) = 0 Multiply (x + 5y) * (3x + 2y) (x(3x + 2y) + 5y * (3x + 2y)) = 0 ((3x * x + 2y * x) + 5y * (3x + 2y)) = 0 Reorder the terms: ((2xy + 3x2) + 5y * (3x + 2y)) = 0 ((2xy + 3x2) + 5y * (3x + 2y)) = 0 (2xy + 3x2 + (3x * 5y + 2y * 5y)) = 0 (2xy + 3x2 + (15xy + 10y2)) = 0 Reorder the terms: (2xy + 15xy + 3x2 + 10y2) = 0 Combine like terms: 2xy + 15xy = 17xy (17xy + 3x2 + 10y2) = 0 Solving 17xy + 3x2 + 10y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + 2y)(x + 5y) = 0Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySubproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {-0.6666666667y, -5y}
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