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Simplifying (3x + -2y)(4x + -1y) = 0 Multiply (3x + -2y) * (4x + -1y) (3x * (4x + -1y) + -2y * (4x + -1y)) = 0 ((4x * 3x + -1y * 3x) + -2y * (4x + -1y)) = 0 Reorder the terms: ((-3xy + 12x2) + -2y * (4x + -1y)) = 0 ((-3xy + 12x2) + -2y * (4x + -1y)) = 0 (-3xy + 12x2 + (4x * -2y + -1y * -2y)) = 0 (-3xy + 12x2 + (-8xy + 2y2)) = 0 Reorder the terms: (-3xy + -8xy + 12x2 + 2y2) = 0 Combine like terms: -3xy + -8xy = -11xy (-11xy + 12x2 + 2y2) = 0 Solving -11xy + 12x2 + 2y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -2y)(4x + -1y) = 0Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve: Simplifying 3x + -2y = 0 Solving 3x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 3x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 3x + 0 = 0 + 2y 3x = 0 + 2y Remove the zero: 3x = 2y Divide each side by '3'. x = 0.6666666667y Simplifying x = 0.6666666667ySubproblem 2
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 = 0.25ySolution
x = {0.6666666667y, 0.25y}
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