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Simplifying (2x + -3y)(5x + -2y) = 0 Multiply (2x + -3y) * (5x + -2y) (2x * (5x + -2y) + -3y * (5x + -2y)) = 0 ((5x * 2x + -2y * 2x) + -3y * (5x + -2y)) = 0 Reorder the terms: ((-4xy + 10x^{2}) + -3y * (5x + -2y)) = 0 ((-4xy + 10x^{2}) + -3y * (5x + -2y)) = 0 (-4xy + 10x^{2}+ (5x * -3y + -2y * -3y)) = 0 (-4xy + 10x^{2}+ (-15xy + 6y^{2})) = 0 Reorder the terms: (-4xy + -15xy + 10x^{2}+ 6y^{2}) = 0 Combine like terms: -4xy + -15xy = -19xy (-19xy + 10x^{2}+ 6y^{2}) = 0 Solving -19xy + 10x^{2}+ 6y^{2}= 0 Solving for variable 'x'. Factor a trinomial. (2x + -3y)(5x + -2y) = 0## Subproblem 1

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 = 1.5y## Subproblem 2

Set the factor '(5x + -2y)' equal to zero and attempt to solve: Simplifying 5x + -2y = 0 Solving 5x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 5x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5x + 0 = 0 + 2y 5x = 0 + 2y Remove the zero: 5x = 2y Divide each side by '5'. x = 0.4y Simplifying x = 0.4y## Solution

x = {1.5y, 0.4y}

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