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Simplifying 60x2 + 3xy + -36y2 = 0 Reorder the terms: 3xy + 60x2 + -36y2 = 0 Solving 3xy + 60x2 + -36y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(xy + 20x2 + -12y2) = 0 Factor a trinomial. 3((4x + -3y)(5x + 4y)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4x + -3y)' equal to zero and attempt to solve: Simplifying 4x + -3y = 0 Solving 4x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. 4x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 4x + 0 = 0 + 3y 4x = 0 + 3y Remove the zero: 4x = 3y Divide each side by '4'. x = 0.75y Simplifying x = 0.75ySubproblem 2
Set the factor '(5x + 4y)' equal to zero and attempt to solve: Simplifying 5x + 4y = 0 Solving 5x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 5x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 5x + 0 = 0 + -4y 5x = 0 + -4y Remove the zero: 5x = -4y Divide each side by '5'. x = -0.8y Simplifying x = -0.8ySolution
x = {0.75y, -0.8y}
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