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Simplifying (x + -4y)(8x + -12y) = 0 Multiply (x + -4y) * (8x + -12y) (x(8x + -12y) + -4y * (8x + -12y)) = 0 ((8x * x + -12y * x) + -4y * (8x + -12y)) = 0 Reorder the terms: ((-12xy + 8x2) + -4y * (8x + -12y)) = 0 ((-12xy + 8x2) + -4y * (8x + -12y)) = 0 (-12xy + 8x2 + (8x * -4y + -12y * -4y)) = 0 (-12xy + 8x2 + (-32xy + 48y2)) = 0 Reorder the terms: (-12xy + -32xy + 8x2 + 48y2) = 0 Combine like terms: -12xy + -32xy = -44xy (-44xy + 8x2 + 48y2) = 0 Solving -44xy + 8x2 + 48y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-11xy + 2x2 + 12y2) = 0 Factor a trinomial. 4((x + -4y)(2x + -3y)) = 0 Ignore the factor 4.Subproblem 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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