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Simplifying (2x + 11y)(4x + 8y) = 0 Multiply (2x + 11y) * (4x + 8y) (2x * (4x + 8y) + 11y * (4x + 8y)) = 0 ((4x * 2x + 8y * 2x) + 11y * (4x + 8y)) = 0 Reorder the terms: ((16xy + 8x2) + 11y * (4x + 8y)) = 0 ((16xy + 8x2) + 11y * (4x + 8y)) = 0 (16xy + 8x2 + (4x * 11y + 8y * 11y)) = 0 (16xy + 8x2 + (44xy + 88y2)) = 0 Reorder the terms: (16xy + 44xy + 8x2 + 88y2) = 0 Combine like terms: 16xy + 44xy = 60xy (60xy + 8x2 + 88y2) = 0 Solving 60xy + 8x2 + 88y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(15xy + 2x2 + 22y2) = 0 Factor a trinomial. 4((x + 2y)(2x + 11y)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(x + 2y)' equal to zero and attempt to solve: Simplifying x + 2y = 0 Solving x + 2y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. x + 2y + -2y = 0 + -2y Combine like terms: 2y + -2y = 0 x + 0 = 0 + -2y x = 0 + -2y Remove the zero: x = -2y Simplifying x = -2ySubproblem 2
Set the factor '(2x + 11y)' equal to zero and attempt to solve: Simplifying 2x + 11y = 0 Solving 2x + 11y = 0 Move all terms containing x to the left, all other terms to the right. Add '-11y' to each side of the equation. 2x + 11y + -11y = 0 + -11y Combine like terms: 11y + -11y = 0 2x + 0 = 0 + -11y 2x = 0 + -11y Remove the zero: 2x = -11y Divide each side by '2'. x = -5.5y Simplifying x = -5.5ySolution
x = {-2y, -5.5y}
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