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Simplifying 6(5x2 + 17xy + 12y2) = 0 Reorder the terms: 6(17xy + 5x2 + 12y2) = 0 (17xy * 6 + 5x2 * 6 + 12y2 * 6) = 0 (102xy + 30x2 + 72y2) = 0 Solving 102xy + 30x2 + 72y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6'. 6(17xy + 5x2 + 12y2) = 0 Factor a trinomial. 6((x + y)(5x + 12y)) = 0 Ignore the factor 6.Subproblem 1
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 = -1ySubproblem 2
Set the factor '(5x + 12y)' equal to zero and attempt to solve: Simplifying 5x + 12y = 0 Solving 5x + 12y = 0 Move all terms containing x to the left, all other terms to the right. Add '-12y' to each side of the equation. 5x + 12y + -12y = 0 + -12y Combine like terms: 12y + -12y = 0 5x + 0 = 0 + -12y 5x = 0 + -12y Remove the zero: 5x = -12y Divide each side by '5'. x = -2.4y Simplifying x = -2.4ySolution
x = {-1y, -2.4y}
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