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Simplifying 40x2y + 10xy + -15y = 0 Reorder the terms: 10xy + 40x2y + -15y = 0 Solving 10xy + 40x2y + -15y = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(2x + 8x2 + -3) = 0 Factor a trinomial. 5y((2x + -1)(4x + 3)) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y = 0 + -1y Remove the zero: 0 = -1y Simplifying 0 = -1y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(2x + -1)' equal to zero and attempt to solve: Simplifying 2x + -1 = 0 Reorder the terms: -1 + 2x = 0 Solving -1 + 2x = 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 + 2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2x = 0 + 1 2x = 0 + 1 Combine like terms: 0 + 1 = 1 2x = 1 Divide each side by '2'. x = 0.5 Simplifying x = 0.5Subproblem 3
Set the factor '(4x + 3)' equal to zero and attempt to solve: Simplifying 4x + 3 = 0 Reorder the terms: 3 + 4x = 0 Solving 3 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4x = 0 + -3 4x = 0 + -3 Combine like terms: 0 + -3 = -3 4x = -3 Divide each side by '4'. x = -0.75 Simplifying x = -0.75Solution
x = {0.5, -0.75}
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