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Simplifying (4x + 5y)(3x + 8y) = 0 Multiply (4x + 5y) * (3x + 8y) (4x * (3x + 8y) + 5y * (3x + 8y)) = 0 ((3x * 4x + 8y * 4x) + 5y * (3x + 8y)) = 0 Reorder the terms: ((32xy + 12x2) + 5y * (3x + 8y)) = 0 ((32xy + 12x2) + 5y * (3x + 8y)) = 0 (32xy + 12x2 + (3x * 5y + 8y * 5y)) = 0 (32xy + 12x2 + (15xy + 40y2)) = 0 Reorder the terms: (32xy + 15xy + 12x2 + 40y2) = 0 Combine like terms: 32xy + 15xy = 47xy (47xy + 12x2 + 40y2) = 0 Solving 47xy + 12x2 + 40y2 = 0 Solving for variable 'x'. Factor a trinomial. (4x + 5y)(3x + 8y) = 0Subproblem 1
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 = -1.25ySubproblem 2
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 = -2.666666667ySolution
x = {-1.25y, -2.666666667y}
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