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Simplifying (3y + 4) * x(2y + -1) = 0 Reorder the terms: (4 + 3y) * x(2y + -1) = 0 Reorder the terms: (4 + 3y) * x(-1 + 2y) = 0 Reorder the terms for easier multiplication: x(4 + 3y)(-1 + 2y) = 0 Multiply (4 + 3y) * (-1 + 2y) x(4(-1 + 2y) + 3y * (-1 + 2y)) = 0 x((-1 * 4 + 2y * 4) + 3y * (-1 + 2y)) = 0 x((-4 + 8y) + 3y * (-1 + 2y)) = 0 x(-4 + 8y + (-1 * 3y + 2y * 3y)) = 0 x(-4 + 8y + (-3y + 6y2)) = 0 Combine like terms: 8y + -3y = 5y x(-4 + 5y + 6y2) = 0 (-4 * x + 5y * x + 6y2 * x) = 0 (-4x + 5xy + 6xy2) = 0 Solving -4x + 5xy + 6xy2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 5y + 6y2) = 0 Factor a trinomial. x((-4 + -3y)(1 + -2y)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-4 + -3y)' equal to zero and attempt to solve: Simplifying -4 + -3y = 0 Solving -4 + -3y = 0 Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -3y = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3y = 0 + 4 -3y = 0 + 4 Combine like terms: 0 + 4 = 4 -3y = 4 Add '3y' to each side of the equation. -3y + 3y = 4 + 3y Combine like terms: -3y + 3y = 0 0 = 4 + 3y Simplifying 0 = 4 + 3y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(1 + -2y)' equal to zero and attempt to solve: Simplifying 1 + -2y = 0 Solving 1 + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2y = 0 + -1 -2y = 0 + -1 Combine like terms: 0 + -1 = -1 -2y = -1 Add '2y' to each side of the equation. -2y + 2y = -1 + 2y Combine like terms: -2y + 2y = 0 0 = -1 + 2y Simplifying 0 = -1 + 2y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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