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Simplifying 6x2(x2 + 2xy + -3y2) = 0 Reorder the terms: 6x2(2xy + x2 + -3y2) = 0 (2xy * 6x2 + x2 * 6x2 + -3y2 * 6x2) = 0 Reorder the terms: (-18x2y2 + 12x3y + 6x4) = 0 (-18x2y2 + 12x3y + 6x4) = 0 Solving -18x2y2 + 12x3y + 6x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '6x2'. 6x2(-3y2 + 2xy + x2) = 0 Factor a trinomial. 6x2((-3y + -1x)(y + -1x)) = 0 Ignore the factor 6.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-3y + -1x)' equal to zero and attempt to solve: Simplifying -3y + -1x = 0 Reorder the terms: -1x + -3y = 0 Solving -1x + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '3y' to each side of the equation. -1x + -3y + 3y = 0 + 3y Combine like terms: -3y + 3y = 0 -1x + 0 = 0 + 3y -1x = 0 + 3y Remove the zero: -1x = 3y Divide each side by '-1'. x = -3y Simplifying x = -3ySubproblem 3
Set the factor '(y + -1x)' equal to zero and attempt to solve: Simplifying y + -1x = 0 Reorder the terms: -1x + y = 0 Solving -1x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -1x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -1x + 0 = 0 + -1y -1x = 0 + -1y Remove the zero: -1x = -1y Divide each side by '-1'. x = y Simplifying x = ySolution
x = {0, -3y, y}
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