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Simplifying (2x + 3y)(10x + 3y) = 0 Multiply (2x + 3y) * (10x + 3y) (2x * (10x + 3y) + 3y * (10x + 3y)) = 0 ((10x * 2x + 3y * 2x) + 3y * (10x + 3y)) = 0 Reorder the terms: ((6xy + 20x2) + 3y * (10x + 3y)) = 0 ((6xy + 20x2) + 3y * (10x + 3y)) = 0 (6xy + 20x2 + (10x * 3y + 3y * 3y)) = 0 (6xy + 20x2 + (30xy + 9y2)) = 0 Reorder the terms: (6xy + 30xy + 20x2 + 9y2) = 0 Combine like terms: 6xy + 30xy = 36xy (36xy + 20x2 + 9y2) = 0 Solving 36xy + 20x2 + 9y2 = 0 Solving for variable 'x'. Factor a trinomial. (10x + 3y)(2x + 3y) = 0Subproblem 1
Set the factor '(10x + 3y)' equal to zero and attempt to solve: Simplifying 10x + 3y = 0 Solving 10x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 10x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 10x + 0 = 0 + -3y 10x = 0 + -3y Remove the zero: 10x = -3y Divide each side by '10'. x = -0.3y Simplifying x = -0.3ySubproblem 2
Set the factor '(2x + 3y)' equal to zero and attempt to solve: Simplifying 2x + 3y = 0 Solving 2x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 2x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 2x + 0 = 0 + -3y 2x = 0 + -3y Remove the zero: 2x = -3y Divide each side by '2'. x = -1.5y Simplifying x = -1.5ySolution
x = {-0.3y, -1.5y}
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