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Simplifying -6y(3x + -5y) + 2(6x + 2y) = 0 (3x * -6y + -5y * -6y) + 2(6x + 2y) = 0 (-18xy + 30y2) + 2(6x + 2y) = 0 -18xy + 30y2 + (6x * 2 + 2y * 2) = 0 -18xy + 30y2 + (12x + 4y) = 0 Reorder the terms: 12x + -18xy + 4y + 30y2 = 0 Solving 12x + -18xy + 4y + 30y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 12x + -18xy + 4y + -4y + 30y2 = 0 + -4y Combine like terms: 4y + -4y = 0 12x + -18xy + 0 + 30y2 = 0 + -4y 12x + -18xy + 30y2 = 0 + -4y Remove the zero: 12x + -18xy + 30y2 = -4y Add '-30y2' to each side of the equation. 12x + -18xy + 30y2 + -30y2 = -4y + -30y2 Combine like terms: 30y2 + -30y2 = 0 12x + -18xy + 0 = -4y + -30y2 12x + -18xy = -4y + -30y2 Reorder the terms: 12x + -18xy + 4y + 30y2 = -4y + 4y + -30y2 + 30y2 Combine like terms: -4y + 4y = 0 12x + -18xy + 4y + 30y2 = 0 + -30y2 + 30y2 12x + -18xy + 4y + 30y2 = -30y2 + 30y2 Combine like terms: -30y2 + 30y2 = 0 12x + -18xy + 4y + 30y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6x + -9xy + 2y + 15y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6x + -9xy + 2y + 15y2)' equal to zero and attempt to solve: Simplifying 6x + -9xy + 2y + 15y2 = 0 Solving 6x + -9xy + 2y + 15y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 6x + -9xy + 2y + -2y + 15y2 = 0 + -2y Combine like terms: 2y + -2y = 0 6x + -9xy + 0 + 15y2 = 0 + -2y 6x + -9xy + 15y2 = 0 + -2y Remove the zero: 6x + -9xy + 15y2 = -2y Add '-15y2' to each side of the equation. 6x + -9xy + 15y2 + -15y2 = -2y + -15y2 Combine like terms: 15y2 + -15y2 = 0 6x + -9xy + 0 = -2y + -15y2 6x + -9xy = -2y + -15y2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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