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Simplifying 7x4 + 23x3y + 6x2y2 = 0 Reorder the terms: 6x2y2 + 23x3y + 7x4 = 0 Solving 6x2y2 + 23x3y + 7x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(6y2 + 23xy + 7x2) = 0 Factor a trinomial. x2((3y + x)(2y + 7x)) = 0Subproblem 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 + x)' equal to zero and attempt to solve: Simplifying 3y + x = 0 Reorder the terms: x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySubproblem 3
Set the factor '(2y + 7x)' equal to zero and attempt to solve: Simplifying 2y + 7x = 0 Reorder the terms: 7x + 2y = 0 Solving 7x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 7x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 7x + 0 = 0 + -2y 7x = 0 + -2y Remove the zero: 7x = -2y Divide each side by '7'. x = -0.2857142857y Simplifying x = -0.2857142857ySolution
x = {0, -3y, -0.2857142857y}
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