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Simplifying 2x2 = 5xy + 12y2 Solving 2x2 = 5xy + 12y2 Solving for variable 'x'. Reorder the terms: -5xy + 2x2 + -12y2 = 5xy + 12y2 + -5xy + -12y2 Reorder the terms: -5xy + 2x2 + -12y2 = 5xy + -5xy + 12y2 + -12y2 Combine like terms: 5xy + -5xy = 0 -5xy + 2x2 + -12y2 = 0 + 12y2 + -12y2 -5xy + 2x2 + -12y2 = 12y2 + -12y2 Combine like terms: 12y2 + -12y2 = 0 -5xy + 2x2 + -12y2 = 0 Factor a trinomial. (x + -4y)(2x + 3y) = 0Subproblem 1
Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4ySubproblem 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 = {4y, -1.5y}
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