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Simplifying (5x + -3y)(5x + -3y) = 0 Multiply (5x + -3y) * (5x + -3y) (5x * (5x + -3y) + -3y * (5x + -3y)) = 0 ((5x * 5x + -3y * 5x) + -3y * (5x + -3y)) = 0 Reorder the terms: ((-15xy + 25x2) + -3y * (5x + -3y)) = 0 ((-15xy + 25x2) + -3y * (5x + -3y)) = 0 (-15xy + 25x2 + (5x * -3y + -3y * -3y)) = 0 (-15xy + 25x2 + (-15xy + 9y2)) = 0 Reorder the terms: (-15xy + -15xy + 25x2 + 9y2) = 0 Combine like terms: -15xy + -15xy = -30xy (-30xy + 25x2 + 9y2) = 0 Solving -30xy + 25x2 + 9y2 = 0 Solving for variable 'x'. Factor a trinomial. (5x + -3y)(5x + -3y) = 0Subproblem 1
Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySubproblem 2
Set the factor '(5x + -3y)' equal to zero and attempt to solve: Simplifying 5x + -3y = 0 Solving 5x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 5x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 5x + 0 = 0 + 3y 5x = 0 + 3y Remove the zero: 5x = 3y Divide each side by '5'. x = 0.6y Simplifying x = 0.6ySolution
x = {0.6y, 0.6y}
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