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Simplifying (3x + -8y)(5x + -2y) = 0 Multiply (3x + -8y) * (5x + -2y) (3x * (5x + -2y) + -8y * (5x + -2y)) = 0 ((5x * 3x + -2y * 3x) + -8y * (5x + -2y)) = 0 Reorder the terms: ((-6xy + 15x2) + -8y * (5x + -2y)) = 0 ((-6xy + 15x2) + -8y * (5x + -2y)) = 0 (-6xy + 15x2 + (5x * -8y + -2y * -8y)) = 0 (-6xy + 15x2 + (-40xy + 16y2)) = 0 Reorder the terms: (-6xy + -40xy + 15x2 + 16y2) = 0 Combine like terms: -6xy + -40xy = -46xy (-46xy + 15x2 + 16y2) = 0 Solving -46xy + 15x2 + 16y2 = 0 Solving for variable 'x'. Factor a trinomial. (3x + -8y)(5x + -2y) = 0Subproblem 1
Set the factor '(3x + -8y)' equal to zero and attempt to solve: Simplifying 3x + -8y = 0 Solving 3x + -8y = 0 Move all terms containing x to the left, all other terms to the right. Add '8y' to each side of the equation. 3x + -8y + 8y = 0 + 8y Combine like terms: -8y + 8y = 0 3x + 0 = 0 + 8y 3x = 0 + 8y Remove the zero: 3x = 8y Divide each side by '3'. x = 2.666666667y Simplifying x = 2.666666667ySubproblem 2
Set the factor '(5x + -2y)' equal to zero and attempt to solve: Simplifying 5x + -2y = 0 Solving 5x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. 5x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 5x + 0 = 0 + 2y 5x = 0 + 2y Remove the zero: 5x = 2y Divide each side by '5'. x = 0.4y Simplifying x = 0.4ySolution
x = {2.666666667y, 0.4y}
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