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Simplifying (3x + -1y)(2x + -2y) = 0 Multiply (3x + -1y) * (2x + -2y) (3x * (2x + -2y) + -1y * (2x + -2y)) = 0 ((2x * 3x + -2y * 3x) + -1y * (2x + -2y)) = 0 Reorder the terms: ((-6xy + 6x2) + -1y * (2x + -2y)) = 0 ((-6xy + 6x2) + -1y * (2x + -2y)) = 0 (-6xy + 6x2 + (2x * -1y + -2y * -1y)) = 0 (-6xy + 6x2 + (-2xy + 2y2)) = 0 Reorder the terms: (-6xy + -2xy + 6x2 + 2y2) = 0 Combine like terms: -6xy + -2xy = -8xy (-8xy + 6x2 + 2y2) = 0 Solving -8xy + 6x2 + 2y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4xy + 3x2 + y2) = 0 Factor a trinomial. 2((x + -1y)(3x + -1y)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(x + -1y)' equal to zero and attempt to solve: Simplifying x + -1y = 0 Solving x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. x + -1y + y = 0 + y Combine like terms: -1y + y = 0 x + 0 = 0 + y x = 0 + y Remove the zero: x = y Simplifying x = ySubproblem 2
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySolution
x = {y, 0.3333333333y}
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