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Simplifying (x + 6y)(7x + 8y) = 0 Multiply (x + 6y) * (7x + 8y) (x(7x + 8y) + 6y * (7x + 8y)) = 0 ((7x * x + 8y * x) + 6y * (7x + 8y)) = 0 Reorder the terms: ((8xy + 7x2) + 6y * (7x + 8y)) = 0 ((8xy + 7x2) + 6y * (7x + 8y)) = 0 (8xy + 7x2 + (7x * 6y + 8y * 6y)) = 0 (8xy + 7x2 + (42xy + 48y2)) = 0 Reorder the terms: (8xy + 42xy + 7x2 + 48y2) = 0 Combine like terms: 8xy + 42xy = 50xy (50xy + 7x2 + 48y2) = 0 Solving 50xy + 7x2 + 48y2 = 0 Solving for variable 'x'. Factor a trinomial. (7x + 8y)(x + 6y) = 0Subproblem 1
Set the factor '(7x + 8y)' equal to zero and attempt to solve: Simplifying 7x + 8y = 0 Solving 7x + 8y = 0 Move all terms containing x to the left, all other terms to the right. Add '-8y' to each side of the equation. 7x + 8y + -8y = 0 + -8y Combine like terms: 8y + -8y = 0 7x + 0 = 0 + -8y 7x = 0 + -8y Remove the zero: 7x = -8y Divide each side by '7'. x = -1.142857143y Simplifying x = -1.142857143ySubproblem 2
Set the factor '(x + 6y)' equal to zero and attempt to solve: Simplifying x + 6y = 0 Solving x + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-6y' to each side of the equation. x + 6y + -6y = 0 + -6y Combine like terms: 6y + -6y = 0 x + 0 = 0 + -6y x = 0 + -6y Remove the zero: x = -6y Simplifying x = -6ySolution
x = {-1.142857143y, -6y}
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