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Simplifying (3x + -1y)(2x + 5y) = 0 Multiply (3x + -1y) * (2x + 5y) (3x * (2x + 5y) + -1y * (2x + 5y)) = 0 ((2x * 3x + 5y * 3x) + -1y * (2x + 5y)) = 0 Reorder the terms: ((15xy + 6x2) + -1y * (2x + 5y)) = 0 ((15xy + 6x2) + -1y * (2x + 5y)) = 0 (15xy + 6x2 + (2x * -1y + 5y * -1y)) = 0 (15xy + 6x2 + (-2xy + -5y2)) = 0 Reorder the terms: (15xy + -2xy + 6x2 + -5y2) = 0 Combine like terms: 15xy + -2xy = 13xy (13xy + 6x2 + -5y2) = 0 Solving 13xy + 6x2 + -5y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -1y)(2x + 5y) = 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 '(2x + 5y)' equal to zero and attempt to solve: Simplifying 2x + 5y = 0 Solving 2x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 2x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 2x + 0 = 0 + -5y 2x = 0 + -5y Remove the zero: 2x = -5y Divide each side by '2'. x = -2.5y Simplifying x = -2.5ySolution
x = {0.3333333333y, -2.5y}
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