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Simplifying (5X + -8Y)(4X + -3Y) = 0 Multiply (5X + -8Y) * (4X + -3Y) (5X * (4X + -3Y) + -8Y * (4X + -3Y)) = 0 ((4X * 5X + -3Y * 5X) + -8Y * (4X + -3Y)) = 0 Reorder the terms: ((-15XY + 20X2) + -8Y * (4X + -3Y)) = 0 ((-15XY + 20X2) + -8Y * (4X + -3Y)) = 0 (-15XY + 20X2 + (4X * -8Y + -3Y * -8Y)) = 0 (-15XY + 20X2 + (-32XY + 24Y2)) = 0 Reorder the terms: (-15XY + -32XY + 20X2 + 24Y2) = 0 Combine like terms: -15XY + -32XY = -47XY (-47XY + 20X2 + 24Y2) = 0 Solving -47XY + 20X2 + 24Y2 = 0 Solving for variable 'X'. Factor a trinomial. (5X + -8Y)(4X + -3Y) = 0Subproblem 1
Set the factor '(5X + -8Y)' equal to zero and attempt to solve: Simplifying 5X + -8Y = 0 Solving 5X + -8Y = 0 Move all terms containing X to the left, all other terms to the right. Add '8Y' to each side of the equation. 5X + -8Y + 8Y = 0 + 8Y Combine like terms: -8Y + 8Y = 0 5X + 0 = 0 + 8Y 5X = 0 + 8Y Remove the zero: 5X = 8Y Divide each side by '5'. X = 1.6Y Simplifying X = 1.6YSubproblem 2
Set the factor '(4X + -3Y)' equal to zero and attempt to solve: Simplifying 4X + -3Y = 0 Solving 4X + -3Y = 0 Move all terms containing X to the left, all other terms to the right. Add '3Y' to each side of the equation. 4X + -3Y + 3Y = 0 + 3Y Combine like terms: -3Y + 3Y = 0 4X + 0 = 0 + 3Y 4X = 0 + 3Y Remove the zero: 4X = 3Y Divide each side by '4'. X = 0.75Y Simplifying X = 0.75YSolution
X = {1.6Y, 0.75Y}
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