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Simplifying (4x + -1y)(3x + y) = 0 Multiply (4x + -1y) * (3x + y) (4x * (3x + y) + -1y * (3x + y)) = 0 ((3x * 4x + y * 4x) + -1y * (3x + y)) = 0 Reorder the terms: ((4xy + 12x2) + -1y * (3x + y)) = 0 ((4xy + 12x2) + -1y * (3x + y)) = 0 (4xy + 12x2 + (3x * -1y + y * -1y)) = 0 (4xy + 12x2 + (-3xy + -1y2)) = 0 Reorder the terms: (4xy + -3xy + 12x2 + -1y2) = 0 Combine like terms: 4xy + -3xy = 1xy (1xy + 12x2 + -1y2) = 0 Solving 1xy + 12x2 + -1y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + -1y)(3x + y) = 0Subproblem 1
Set the factor '(4x + -1y)' equal to zero and attempt to solve: Simplifying 4x + -1y = 0 Solving 4x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 4x + -1y + y = 0 + y Combine like terms: -1y + y = 0 4x + 0 = 0 + y 4x = 0 + y Remove the zero: 4x = y Divide each side by '4'. x = 0.25y Simplifying x = 0.25ySubproblem 2
Set the factor '(3x + y)' equal to zero and attempt to solve: Simplifying 3x + y = 0 Solving 3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 3x + 0 = 0 + -1y 3x = 0 + -1y Remove the zero: 3x = -1y Divide each side by '3'. x = -0.3333333333y Simplifying x = -0.3333333333ySolution
x = {0.25y, -0.3333333333y}
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