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Simplifying (4x + 5y)(x + y) = 0 Multiply (4x + 5y) * (x + y) (4x * (x + y) + 5y * (x + y)) = 0 ((x * 4x + y * 4x) + 5y * (x + y)) = 0 Reorder the terms: ((4xy + 4x2) + 5y * (x + y)) = 0 ((4xy + 4x2) + 5y * (x + y)) = 0 (4xy + 4x2 + (x * 5y + y * 5y)) = 0 (4xy + 4x2 + (5xy + 5y2)) = 0 Reorder the terms: (4xy + 5xy + 4x2 + 5y2) = 0 Combine like terms: 4xy + 5xy = 9xy (9xy + 4x2 + 5y2) = 0 Solving 9xy + 4x2 + 5y2 = 0 Solving for variable 'x'. Factor a trinomial. (x + y)(4x + 5y) = 0Subproblem 1
Set the factor '(x + y)' equal to zero and attempt to solve: Simplifying x + y = 0 Solving x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 x + 0 = 0 + -1y x = 0 + -1y Remove the zero: x = -1y Simplifying x = -1ySubproblem 2
Set the factor '(4x + 5y)' equal to zero and attempt to solve: Simplifying 4x + 5y = 0 Solving 4x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 4x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 4x + 0 = 0 + -5y 4x = 0 + -5y Remove the zero: 4x = -5y Divide each side by '4'. x = -1.25y Simplifying x = -1.25ySolution
x = {-1y, -1.25y}
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