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Simplifying 4x4 + 17x3y + 15x2y2 = 0 Reorder the terms: 15x2y2 + 17x3y + 4x4 = 0 Solving 15x2y2 + 17x3y + 4x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x2'. x2(15y2 + 17xy + 4x2) = 0 Factor a trinomial. x2((3y + x)(5y + 4x)) = 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 '(5y + 4x)' equal to zero and attempt to solve: Simplifying 5y + 4x = 0 Reorder the terms: 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySolution
x = {0, -3y, -1.25y}
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