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Simplifying 3x(3x + -2y) + -5x(6y + -1x) + 6xy = 0 (3x * 3x + -2y * 3x) + -5x(6y + -1x) + 6xy = 0 Reorder the terms: (-6xy + 9x2) + -5x(6y + -1x) + 6xy = 0 (-6xy + 9x2) + -5x(6y + -1x) + 6xy = 0 Reorder the terms: -6xy + 9x2 + -5x(-1x + 6y) + 6xy = 0 -6xy + 9x2 + (-1x * -5x + 6y * -5x) + 6xy = 0 Reorder the terms: -6xy + 9x2 + (-30xy + 5x2) + 6xy = 0 -6xy + 9x2 + (-30xy + 5x2) + 6xy = 0 Reorder the terms: -6xy + -30xy + 6xy + 9x2 + 5x2 = 0 Combine like terms: -6xy + -30xy = -36xy -36xy + 6xy + 9x2 + 5x2 = 0 Combine like terms: -36xy + 6xy = -30xy -30xy + 9x2 + 5x2 = 0 Combine like terms: 9x2 + 5x2 = 14x2 -30xy + 14x2 = 0 Solving -30xy + 14x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-15y + 7x) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-15y + 7x)' equal to zero and attempt to solve: Simplifying -15y + 7x = 0 Reorder the terms: 7x + -15y = 0 Solving 7x + -15y = 0 Move all terms containing x to the left, all other terms to the right. Add '15y' to each side of the equation. 7x + -15y + 15y = 0 + 15y Combine like terms: -15y + 15y = 0 7x + 0 = 0 + 15y 7x = 0 + 15y Remove the zero: 7x = 15y Divide each side by '7'. x = 2.142857143y Simplifying x = 2.142857143ySolution
x = {0, 2.142857143y}
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