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Simplifying x(x + -2y) + -5y(3x + -6y) = 0 (x * x + -2y * x) + -5y(3x + -6y) = 0 Reorder the terms: (-2xy + x2) + -5y(3x + -6y) = 0 (-2xy + x2) + -5y(3x + -6y) = 0 -2xy + x2 + (3x * -5y + -6y * -5y) = 0 -2xy + x2 + (-15xy + 30y2) = 0 Reorder the terms: -2xy + -15xy + x2 + 30y2 = 0 Combine like terms: -2xy + -15xy = -17xy -17xy + x2 + 30y2 = 0 Solving -17xy + x2 + 30y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -15y)(x + -2y) = 0Subproblem 1
Set the factor '(x + -15y)' equal to zero and attempt to solve: Simplifying x + -15y = 0 Solving x + -15y = 0 Move all terms containing x to the left, all other terms to the right. Add '15y' to each side of the equation. x + -15y + 15y = 0 + 15y Combine like terms: -15y + 15y = 0 x + 0 = 0 + 15y x = 0 + 15y Remove the zero: x = 15y Simplifying x = 15ySubproblem 2
Set the factor '(x + -2y)' equal to zero and attempt to solve: Simplifying x + -2y = 0 Solving x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 x + 0 = 0 + 2y x = 0 + 2y Remove the zero: x = 2y Simplifying x = 2ySolution
x = {15y, 2y}
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