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Simplifying (3x + -1y)(3x + 7y) = 0 Multiply (3x + -1y) * (3x + 7y) (3x * (3x + 7y) + -1y * (3x + 7y)) = 0 ((3x * 3x + 7y * 3x) + -1y * (3x + 7y)) = 0 Reorder the terms: ((21xy + 9x2) + -1y * (3x + 7y)) = 0 ((21xy + 9x2) + -1y * (3x + 7y)) = 0 (21xy + 9x2 + (3x * -1y + 7y * -1y)) = 0 (21xy + 9x2 + (-3xy + -7y2)) = 0 Reorder the terms: (21xy + -3xy + 9x2 + -7y2) = 0 Combine like terms: 21xy + -3xy = 18xy (18xy + 9x2 + -7y2) = 0 Solving 18xy + 9x2 + -7y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -1y)(3x + 7y) = 0Subproblem 1
Set the factor '(3x + -1y)' equal to zero and attempt to solve: Simplifying 3x + -1y = 0 Solving 3x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 3x + -1y + y = 0 + y Combine like terms: -1y + y = 0 3x + 0 = 0 + y 3x = 0 + y Remove the zero: 3x = y Divide each side by '3'. x = 0.3333333333y Simplifying x = 0.3333333333ySubproblem 2
Set the factor '(3x + 7y)' equal to zero and attempt to solve: Simplifying 3x + 7y = 0 Solving 3x + 7y = 0 Move all terms containing x to the left, all other terms to the right. Add '-7y' to each side of the equation. 3x + 7y + -7y = 0 + -7y Combine like terms: 7y + -7y = 0 3x + 0 = 0 + -7y 3x = 0 + -7y Remove the zero: 3x = -7y Divide each side by '3'. x = -2.333333333y Simplifying x = -2.333333333ySolution
x = {0.3333333333y, -2.333333333y}
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