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Simplifying (x + 2y) * and(2x + -3y) = 0 Reorder the terms for easier multiplication: adn(x + 2y)(2x + -3y) = 0 Multiply (x + 2y) * (2x + -3y) adn(x(2x + -3y) + 2y * (2x + -3y)) = 0 adn((2x * x + -3y * x) + 2y * (2x + -3y)) = 0 Reorder the terms: adn((-3xy + 2x2) + 2y * (2x + -3y)) = 0 adn((-3xy + 2x2) + 2y * (2x + -3y)) = 0 adn(-3xy + 2x2 + (2x * 2y + -3y * 2y)) = 0 adn(-3xy + 2x2 + (4xy + -6y2)) = 0 Reorder the terms: adn(-3xy + 4xy + 2x2 + -6y2) = 0 Combine like terms: -3xy + 4xy = 1xy adn(1xy + 2x2 + -6y2) = 0 (1xy * adn + 2x2 * adn + -6y2 * adn) = 0 (1adnxy + 2adnx2 + -6adny2) = 0 Solving 1adnxy + 2adnx2 + -6adny2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'adn'. adn(xy + 2x2 + -6y2) = 0 Factor a trinomial. adn((2x + -3y)(x + 2y)) = 0Subproblem 1
Set the factor 'adn' equal to zero and attempt to solve: Simplifying adn = 0 Solving adn = 0 Move all terms containing a to the left, all other terms to the right. Simplifying adn = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 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 a to the left, all other terms to the right. Add '-2x' to each side of the equation. 2x + -2x + -3y = 0 + -2x Combine like terms: 2x + -2x = 0 0 + -3y = 0 + -2x -3y = 0 + -2x Remove the zero: -3y = -2x Add '3y' to each side of the equation. -3y + 3y = -2x + 3y Combine like terms: -3y + 3y = 0 0 = -2x + 3y Simplifying 0 = -2x + 3y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x + 2y = 0 + -1x Combine like terms: x + -1x = 0 0 + 2y = 0 + -1x 2y = 0 + -1x Remove the zero: 2y = -1x Add '-2y' to each side of the equation. 2y + -2y = -1x + -2y Combine like terms: 2y + -2y = 0 0 = -1x + -2y Simplifying 0 = -1x + -2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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