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