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Simplifying (7x + 5y)(2x + -3y) = 0 Multiply (7x + 5y) * (2x + -3y) (7x * (2x + -3y) + 5y * (2x + -3y)) = 0 ((2x * 7x + -3y * 7x) + 5y * (2x + -3y)) = 0 Reorder the terms: ((-21xy + 14x2) + 5y * (2x + -3y)) = 0 ((-21xy + 14x2) + 5y * (2x + -3y)) = 0 (-21xy + 14x2 + (2x * 5y + -3y * 5y)) = 0 (-21xy + 14x2 + (10xy + -15y2)) = 0 Reorder the terms: (-21xy + 10xy + 14x2 + -15y2) = 0 Combine like terms: -21xy + 10xy = -11xy (-11xy + 14x2 + -15y2) = 0 Solving -11xy + 14x2 + -15y2 = 0 Solving for variable 'x'. Factor a trinomial. (2x + -3y)(7x + 5y) = 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 '(7x + 5y)' equal to zero and attempt to solve: Simplifying 7x + 5y = 0 Solving 7x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 7x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 7x + 0 = 0 + -5y 7x = 0 + -5y Remove the zero: 7x = -5y Divide each side by '7'. x = -0.7142857143y Simplifying x = -0.7142857143ySolution
x = {1.5y, -0.7142857143y}
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