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Simplifying 3x2 + -15xy + 2xy + -10y2 = 0 Reorder the terms: -15xy + 2xy + 3x2 + -10y2 = 0 Combine like terms: -15xy + 2xy = -13xy -13xy + 3x2 + -10y2 = 0 Solving -13xy + 3x2 + -10y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -5y)(3x + 2y) = 0Subproblem 1
Set the factor '(x + -5y)' equal to zero and attempt to solve: Simplifying x + -5y = 0 Solving x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 x + 0 = 0 + 5y x = 0 + 5y Remove the zero: x = 5y Simplifying x = 5ySubproblem 2
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySolution
x = {5y, -0.6666666667y}
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