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Simplifying 0 = 20x2y + -42xy + -20y Reorder the terms: 0 = -42xy + 20x2y + -20y Solving 0 = -42xy + 20x2y + -20y Solving for variable 'x'. Remove the zero: 42xy + -20x2y + 20y = -42xy + 20x2y + -20y + 42xy + -20x2y + 20y Reorder the terms: 42xy + -20x2y + 20y = -42xy + 42xy + 20x2y + -20x2y + -20y + 20y Combine like terms: -42xy + 42xy = 0 42xy + -20x2y + 20y = 0 + 20x2y + -20x2y + -20y + 20y 42xy + -20x2y + 20y = 20x2y + -20x2y + -20y + 20y Combine like terms: 20x2y + -20x2y = 0 42xy + -20x2y + 20y = 0 + -20y + 20y 42xy + -20x2y + 20y = -20y + 20y Combine like terms: -20y + 20y = 0 42xy + -20x2y + 20y = 0 Factor out the Greatest Common Factor (GCF), '2y'. 2y(21x + -10x2 + 10) = 0 Factor a trinomial. 2y((-5x + -2)(2x + -5)) = 0 Ignore the factor 2.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 '(-5x + -2)' equal to zero and attempt to solve: Simplifying -5x + -2 = 0 Reorder the terms: -2 + -5x = 0 Solving -2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -5x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5x = 0 + 2 -5x = 0 + 2 Combine like terms: 0 + 2 = 2 -5x = 2 Divide each side by '-5'. x = -0.4 Simplifying x = -0.4Subproblem 3
Set the factor '(2x + -5)' equal to zero and attempt to solve: Simplifying 2x + -5 = 0 Reorder the terms: -5 + 2x = 0 Solving -5 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x = 0 + 5 2x = 0 + 5 Combine like terms: 0 + 5 = 5 2x = 5 Divide each side by '2'. x = 2.5 Simplifying x = 2.5Solution
x = {-0.4, 2.5}
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