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Simplifying (3x + 7y)(7x + 5y) = 0 Multiply (3x + 7y) * (7x + 5y) (3x * (7x + 5y) + 7y * (7x + 5y)) = 0 ((7x * 3x + 5y * 3x) + 7y * (7x + 5y)) = 0 Reorder the terms: ((15xy + 21x2) + 7y * (7x + 5y)) = 0 ((15xy + 21x2) + 7y * (7x + 5y)) = 0 (15xy + 21x2 + (7x * 7y + 5y * 7y)) = 0 (15xy + 21x2 + (49xy + 35y2)) = 0 Reorder the terms: (15xy + 49xy + 21x2 + 35y2) = 0 Combine like terms: 15xy + 49xy = 64xy (64xy + 21x2 + 35y2) = 0 Solving 64xy + 21x2 + 35y2 = 0 Solving for variable 'x'. Factor a trinomial. (7x + 5y)(3x + 7y) = 0Subproblem 1
Set the factor '(7x + 5y)' equal to zero and attempt to solve: Simplifying 7x + 5y = 0 Solving 7x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 7x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 7x + 0 = 0 + -5y 7x = 0 + -5y Remove the zero: 7x = -5y Divide each side by '7'. x = -0.7142857143y Simplifying x = -0.7142857143ySubproblem 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 = {-0.7142857143y, -2.333333333y}
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