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Simplifying (x + 5y)(7x + 3y) = 0 Multiply (x + 5y) * (7x + 3y) (x(7x + 3y) + 5y * (7x + 3y)) = 0 ((7x * x + 3y * x) + 5y * (7x + 3y)) = 0 Reorder the terms: ((3xy + 7x2) + 5y * (7x + 3y)) = 0 ((3xy + 7x2) + 5y * (7x + 3y)) = 0 (3xy + 7x2 + (7x * 5y + 3y * 5y)) = 0 (3xy + 7x2 + (35xy + 15y2)) = 0 Reorder the terms: (3xy + 35xy + 7x2 + 15y2) = 0 Combine like terms: 3xy + 35xy = 38xy (38xy + 7x2 + 15y2) = 0 Solving 38xy + 7x2 + 15y2 = 0 Solving for variable 'x'. Factor a trinomial. (7x + 3y)(x + 5y) = 0Subproblem 1
Set the factor '(7x + 3y)' equal to zero and attempt to solve: Simplifying 7x + 3y = 0 Solving 7x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 7x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 7x + 0 = 0 + -3y 7x = 0 + -3y Remove the zero: 7x = -3y Divide each side by '7'. x = -0.4285714286y Simplifying x = -0.4285714286ySubproblem 2
Set the factor '(x + 5y)' equal to zero and attempt to solve: Simplifying x + 5y = 0 Solving x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 x + 0 = 0 + -5y x = 0 + -5y Remove the zero: x = -5y Simplifying x = -5ySolution
x = {-0.4285714286y, -5y}
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