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Simplifying (3x + -5y)(3x + 4y) = 0 Multiply (3x + -5y) * (3x + 4y) (3x * (3x + 4y) + -5y * (3x + 4y)) = 0 ((3x * 3x + 4y * 3x) + -5y * (3x + 4y)) = 0 Reorder the terms: ((12xy + 9x2) + -5y * (3x + 4y)) = 0 ((12xy + 9x2) + -5y * (3x + 4y)) = 0 (12xy + 9x2 + (3x * -5y + 4y * -5y)) = 0 (12xy + 9x2 + (-15xy + -20y2)) = 0 Reorder the terms: (12xy + -15xy + 9x2 + -20y2) = 0 Combine like terms: 12xy + -15xy = -3xy (-3xy + 9x2 + -20y2) = 0 Solving -3xy + 9x2 + -20y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -5y)(3x + 4y) = 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 '(3x + 4y)' equal to zero and attempt to solve: Simplifying 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySolution
x = {1.666666667y, -1.333333333y}
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