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Simplifying (7x + -1y)(2x + 3y) = 0 Multiply (7x + -1y) * (2x + 3y) (7x * (2x + 3y) + -1y * (2x + 3y)) = 0 ((2x * 7x + 3y * 7x) + -1y * (2x + 3y)) = 0 Reorder the terms: ((21xy + 14x2) + -1y * (2x + 3y)) = 0 ((21xy + 14x2) + -1y * (2x + 3y)) = 0 (21xy + 14x2 + (2x * -1y + 3y * -1y)) = 0 (21xy + 14x2 + (-2xy + -3y2)) = 0 Reorder the terms: (21xy + -2xy + 14x2 + -3y2) = 0 Combine like terms: 21xy + -2xy = 19xy (19xy + 14x2 + -3y2) = 0 Solving 19xy + 14x2 + -3y2 = 0 Solving for variable 'x'. Factor a trinomial. (7x + -1y)(2x + 3y) = 0Subproblem 1
Set the factor '(7x + -1y)' equal to zero and attempt to solve: Simplifying 7x + -1y = 0 Solving 7x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 7x + -1y + y = 0 + y Combine like terms: -1y + y = 0 7x + 0 = 0 + y 7x = 0 + y Remove the zero: 7x = y Divide each side by '7'. x = 0.1428571429y Simplifying x = 0.1428571429ySubproblem 2
Set the factor '(2x + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 2x + 0 = 0 + -3y 2x = 0 + -3y Remove the zero: 2x = -3y Divide each side by '2'. x = -1.5y Simplifying x = -1.5ySolution
x = {0.1428571429y, -1.5y}
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