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Simplifying 27x4 + -48x2y2 = 0 Reorder the terms: -48x2y2 + 27x4 = 0 Solving -48x2y2 + 27x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x2'. 3x2(-16y2 + 9x2) = 0 Factor a difference between two squares. 3x2((4y + 3x)(-4y + 3x)) = 0 Ignore the factor 3.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 '(4y + 3x)' equal to zero and attempt to solve: Simplifying 4y + 3x = 0 Reorder the terms: 3x + 4y = 0 Solving 3x + 4y = 0 Move all terms containing x to the left, all other terms to the right. Add '-4y' to each side of the equation. 3x + 4y + -4y = 0 + -4y Combine like terms: 4y + -4y = 0 3x + 0 = 0 + -4y 3x = 0 + -4y Remove the zero: 3x = -4y Divide each side by '3'. x = -1.333333333y Simplifying x = -1.333333333ySubproblem 3
Set the factor '(-4y + 3x)' equal to zero and attempt to solve: Simplifying -4y + 3x = 0 Reorder the terms: 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333ySolution
x = {0, -1.333333333y, 1.333333333y}
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