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Simplifying (-3x + y)(2x + -5y) = 0 Multiply (-3x + y) * (2x + -5y) (-3x * (2x + -5y) + y(2x + -5y)) = 0 ((2x * -3x + -5y * -3x) + y(2x + -5y)) = 0 Reorder the terms: ((15xy + -6x2) + y(2x + -5y)) = 0 ((15xy + -6x2) + y(2x + -5y)) = 0 (15xy + -6x2 + (2x * y + -5y * y)) = 0 (15xy + -6x2 + (2xy + -5y2)) = 0 Reorder the terms: (15xy + 2xy + -6x2 + -5y2) = 0 Combine like terms: 15xy + 2xy = 17xy (17xy + -6x2 + -5y2) = 0 Solving 17xy + -6x2 + -5y2 = 0 Solving for variable 'x'. Factor a trinomial. (-3x + y)(2x + -5y) = 0Subproblem 1
Set the factor '(-3x + y)' equal to zero and attempt to solve: Simplifying -3x + y = 0 Solving -3x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. -3x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 -3x + 0 = 0 + -1y -3x = 0 + -1y Remove the zero: -3x = -1y Divide each side by '-3'. x = 0.3333333333y Simplifying x = 0.3333333333ySubproblem 2
Set the factor '(2x + -5y)' equal to zero and attempt to solve: Simplifying 2x + -5y = 0 Solving 2x + -5y = 0 Move all terms containing x to the left, all other terms to the right. Add '5y' to each side of the equation. 2x + -5y + 5y = 0 + 5y Combine like terms: -5y + 5y = 0 2x + 0 = 0 + 5y 2x = 0 + 5y Remove the zero: 2x = 5y Divide each side by '2'. x = 2.5y Simplifying x = 2.5ySolution
x = {0.3333333333y, 2.5y}
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