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Simplifying (4x + -6y)(2x + 6y) = 0 Multiply (4x + -6y) * (2x + 6y) (4x * (2x + 6y) + -6y * (2x + 6y)) = 0 ((2x * 4x + 6y * 4x) + -6y * (2x + 6y)) = 0 Reorder the terms: ((24xy + 8x2) + -6y * (2x + 6y)) = 0 ((24xy + 8x2) + -6y * (2x + 6y)) = 0 (24xy + 8x2 + (2x * -6y + 6y * -6y)) = 0 (24xy + 8x2 + (-12xy + -36y2)) = 0 Reorder the terms: (24xy + -12xy + 8x2 + -36y2) = 0 Combine like terms: 24xy + -12xy = 12xy (12xy + 8x2 + -36y2) = 0 Solving 12xy + 8x2 + -36y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3xy + 2x2 + -9y2) = 0 Factor a trinomial. 4((2x + -3y)(x + 3y)) = 0 Ignore the factor 4.Subproblem 1
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 = 1.5ySubproblem 2
Set the factor '(x + 3y)' equal to zero and attempt to solve: Simplifying x + 3y = 0 Solving x + 3y = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. x + 3y + -3y = 0 + -3y Combine like terms: 3y + -3y = 0 x + 0 = 0 + -3y x = 0 + -3y Remove the zero: x = -3y Simplifying x = -3ySolution
x = {1.5y, -3y}
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