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Simplifying (4x + -1y)(x + 3y) = 0 Multiply (4x + -1y) * (x + 3y) (4x * (x + 3y) + -1y * (x + 3y)) = 0 ((x * 4x + 3y * 4x) + -1y * (x + 3y)) = 0 Reorder the terms: ((12xy + 4x2) + -1y * (x + 3y)) = 0 ((12xy + 4x2) + -1y * (x + 3y)) = 0 (12xy + 4x2 + (x * -1y + 3y * -1y)) = 0 (12xy + 4x2 + (-1xy + -3y2)) = 0 Reorder the terms: (12xy + -1xy + 4x2 + -3y2) = 0 Combine like terms: 12xy + -1xy = 11xy (11xy + 4x2 + -3y2) = 0 Solving 11xy + 4x2 + -3y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + -1y)(x + 3y) = 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 '(x + 3y)' equal to zero and attempt to solve: Simplifying 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 = -3ySolution
x = {0.25y, -3y}
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