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Simplifying 4(12x2 + 20xy + 8y2) = 0 Reorder the terms: 4(20xy + 12x2 + 8y2) = 0 (20xy * 4 + 12x2 * 4 + 8y2 * 4) = 0 (80xy + 48x2 + 32y2) = 0 Solving 80xy + 48x2 + 32y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '16'. 16(5xy + 3x2 + 2y2) = 0 Factor a trinomial. 16((3x + 2y)(x + y)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(3x + 2y)' equal to zero and attempt to solve: Simplifying 3x + 2y = 0 Solving 3x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 3x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 3x + 0 = 0 + -2y 3x = 0 + -2y Remove the zero: 3x = -2y Divide each side by '3'. x = -0.6666666667y Simplifying x = -0.6666666667ySubproblem 2
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySolution
x = {-0.6666666667y, -1y}
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