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Simplifying 6x2 + 41xy + -30y2 = 0 Reorder the terms: 41xy + 6x2 + -30y2 = 0 Solving 41xy + 6x2 + -30y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -2y)(2x + 15y) = 0Subproblem 1
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 = 0.6666666667ySubproblem 2
Set the factor '(2x + 15y)' equal to zero and attempt to solve: Simplifying 2x + 15y = 0 Solving 2x + 15y = 0 Move all terms containing x to the left, all other terms to the right. Add '-15y' to each side of the equation. 2x + 15y + -15y = 0 + -15y Combine like terms: 15y + -15y = 0 2x + 0 = 0 + -15y 2x = 0 + -15y Remove the zero: 2x = -15y Divide each side by '2'. x = -7.5y Simplifying x = -7.5ySolution
x = {0.6666666667y, -7.5y}
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