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Simplifying 3x2 + 12xy + 12y2 = 0 Reorder the terms: 12xy + 3x2 + 12y2 = 0 Solving 12xy + 3x2 + 12y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4xy + x2 + 4y2) = 0 Factor a trinomial. 3((x + 2y)(x + 2y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySubproblem 2
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySolution
x = {-2y, -2y}
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