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Simplifying (3x + -5y)(4x + -3y) = 0 Multiply (3x + -5y) * (4x + -3y) (3x * (4x + -3y) + -5y * (4x + -3y)) = 0 ((4x * 3x + -3y * 3x) + -5y * (4x + -3y)) = 0 Reorder the terms: ((-9xy + 12x2) + -5y * (4x + -3y)) = 0 ((-9xy + 12x2) + -5y * (4x + -3y)) = 0 (-9xy + 12x2 + (4x * -5y + -3y * -5y)) = 0 (-9xy + 12x2 + (-20xy + 15y2)) = 0 Reorder the terms: (-9xy + -20xy + 12x2 + 15y2) = 0 Combine like terms: -9xy + -20xy = -29xy (-29xy + 12x2 + 15y2) = 0 Solving -29xy + 12x2 + 15y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -5y)(4x + -3y) = 0Subproblem 1
Set the factor '(3x + -5y)' equal to zero and attempt to solve: Simplifying 3x + -5y = 0 Solving 3x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 3x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 3x + 0 = 0 + 5y 3x = 0 + 5y Remove the zero: 3x = 5y Divide each side by '3'. x = 1.666666667y Simplifying x = 1.666666667ySubproblem 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 = {1.666666667y, 0.75y}
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