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Simplifying (5x + -2y)(2x + -3y) = 0 Multiply (5x + -2y) * (2x + -3y) (5x * (2x + -3y) + -2y * (2x + -3y)) = 0 ((2x * 5x + -3y * 5x) + -2y * (2x + -3y)) = 0 Reorder the terms: ((-15xy + 10x2) + -2y * (2x + -3y)) = 0 ((-15xy + 10x2) + -2y * (2x + -3y)) = 0 (-15xy + 10x2 + (2x * -2y + -3y * -2y)) = 0 (-15xy + 10x2 + (-4xy + 6y2)) = 0 Reorder the terms: (-15xy + -4xy + 10x2 + 6y2) = 0 Combine like terms: -15xy + -4xy = -19xy (-19xy + 10x2 + 6y2) = 0 Solving -19xy + 10x2 + 6y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -3y)(5x + -2y) = 0Subproblem 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 = 1.5ySubproblem 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 = 0.4ySolution
x = {1.5y, 0.4y}
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