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Simplifying (3x + -2y)(6x + y) = 0 Multiply (3x + -2y) * (6x + y) (3x * (6x + y) + -2y * (6x + y)) = 0 ((6x * 3x + y * 3x) + -2y * (6x + y)) = 0 Reorder the terms: ((3xy + 18x2) + -2y * (6x + y)) = 0 ((3xy + 18x2) + -2y * (6x + y)) = 0 (3xy + 18x2 + (6x * -2y + y * -2y)) = 0 (3xy + 18x2 + (-12xy + -2y2)) = 0 Reorder the terms: (3xy + -12xy + 18x2 + -2y2) = 0 Combine like terms: 3xy + -12xy = -9xy (-9xy + 18x2 + -2y2) = 0 Solving -9xy + 18x2 + -2y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -2y)(6x + y) = 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 '(6x + y)' equal to zero and attempt to solve: Simplifying 6x + y = 0 Solving 6x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 6x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 6x + 0 = 0 + -1y 6x = 0 + -1y Remove the zero: 6x = -1y Divide each side by '6'. x = -0.1666666667y Simplifying x = -0.1666666667ySolution
x = {0.6666666667y, -0.1666666667y}
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