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Simplifying 12x2 + 12xy + 3y2 = 0 Reorder the terms: 12xy + 12x2 + 3y2 = 0 Solving 12xy + 12x2 + 3y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(4xy + 4x2 + y2) = 0 Factor a trinomial. 3((2x + y)(2x + y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySubproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5ySolution
x = {-0.5y, -0.5y}
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