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Simplifying 6x2 + -30xy + 5xy + -25y2 = 0 Reorder the terms: -30xy + 5xy + 6x2 + -25y2 = 0 Combine like terms: -30xy + 5xy = -25xy -25xy + 6x2 + -25y2 = 0 Solving -25xy + 6x2 + -25y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -5y)(6x + 5y) = 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 '(6x + 5y)' equal to zero and attempt to solve: Simplifying 6x + 5y = 0 Solving 6x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 6x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 6x + 0 = 0 + -5y 6x = 0 + -5y Remove the zero: 6x = -5y Divide each side by '6'. x = -0.8333333333y Simplifying x = -0.8333333333ySolution
x = {5y, -0.8333333333y}
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