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Simplifying (x + -6y)(7x + 2y) = 0 Multiply (x + -6y) * (7x + 2y) (x(7x + 2y) + -6y * (7x + 2y)) = 0 ((7x * x + 2y * x) + -6y * (7x + 2y)) = 0 Reorder the terms: ((2xy + 7x2) + -6y * (7x + 2y)) = 0 ((2xy + 7x2) + -6y * (7x + 2y)) = 0 (2xy + 7x2 + (7x * -6y + 2y * -6y)) = 0 (2xy + 7x2 + (-42xy + -12y2)) = 0 Reorder the terms: (2xy + -42xy + 7x2 + -12y2) = 0 Combine like terms: 2xy + -42xy = -40xy (-40xy + 7x2 + -12y2) = 0 Solving -40xy + 7x2 + -12y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + -6y)(7x + 2y) = 0Subproblem 1
Set the factor '(x + -6y)' equal to zero and attempt to solve: Simplifying x + -6y = 0 Solving x + -6y = 0 Move all terms containing x to the left, all other terms to the right. Add '6y' to each side of the equation. x + -6y + 6y = 0 + 6y Combine like terms: -6y + 6y = 0 x + 0 = 0 + 6y x = 0 + 6y Remove the zero: x = 6y Simplifying x = 6ySubproblem 2
Set the factor '(7x + 2y)' equal to zero and attempt to solve: Simplifying 7x + 2y = 0 Solving 7x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 7x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 7x + 0 = 0 + -2y 7x = 0 + -2y Remove the zero: 7x = -2y Divide each side by '7'. x = -0.2857142857y Simplifying x = -0.2857142857ySolution
x = {6y, -0.2857142857y}
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