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Simplifying (-3x + 4y)(2x + 5y) = 0 Multiply (-3x + 4y) * (2x + 5y) (-3x * (2x + 5y) + 4y * (2x + 5y)) = 0 ((2x * -3x + 5y * -3x) + 4y * (2x + 5y)) = 0 Reorder the terms: ((-15xy + -6x2) + 4y * (2x + 5y)) = 0 ((-15xy + -6x2) + 4y * (2x + 5y)) = 0 (-15xy + -6x2 + (2x * 4y + 5y * 4y)) = 0 (-15xy + -6x2 + (8xy + 20y2)) = 0 Reorder the terms: (-15xy + 8xy + -6x2 + 20y2) = 0 Combine like terms: -15xy + 8xy = -7xy (-7xy + -6x2 + 20y2) = 0 Solving -7xy + -6x2 + 20y2 = 0 Solving for variable 'x'. Factor a trinomial. (-2x + -5y)(3x + -4y) = 0Subproblem 1
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 = -2.5ySubproblem 2
Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333ySolution
x = {-2.5y, 1.333333333y}
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