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Simplifying (2x + 4)(3y + 1) = 0 Reorder the terms: (4 + 2x)(3y + 1) = 0 Reorder the terms: (4 + 2x)(1 + 3y) = 0 Multiply (4 + 2x) * (1 + 3y) (4(1 + 3y) + 2x * (1 + 3y)) = 0 ((1 * 4 + 3y * 4) + 2x * (1 + 3y)) = 0 ((4 + 12y) + 2x * (1 + 3y)) = 0 (4 + 12y + (1 * 2x + 3y * 2x)) = 0 (4 + 12y + (2x + 6xy)) = 0 Reorder the terms: (4 + 2x + 6xy + 12y) = 0 (4 + 2x + 6xy + 12y) = 0 Solving 4 + 2x + 6xy + 12y = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 2x + 6xy + -4 + 12y = 0 + -4 Reorder the terms: 4 + -4 + 2x + 6xy + 12y = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 2x + 6xy + 12y = 0 + -4 2x + 6xy + 12y = 0 + -4 Combine like terms: 0 + -4 = -4 2x + 6xy + 12y = -4 Add '-12y' to each side of the equation. 2x + 6xy + 12y + -12y = -4 + -12y Combine like terms: 12y + -12y = 0 2x + 6xy + 0 = -4 + -12y 2x + 6xy = -4 + -12y Reorder the terms: 4 + 2x + 6xy + 12y = -4 + -12y + 4 + 12y Reorder the terms: 4 + 2x + 6xy + 12y = -4 + 4 + -12y + 12y Combine like terms: -4 + 4 = 0 4 + 2x + 6xy + 12y = 0 + -12y + 12y 4 + 2x + 6xy + 12y = -12y + 12y Combine like terms: -12y + 12y = 0 4 + 2x + 6xy + 12y = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + x + 3xy + 6y) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + x + 3xy + 6y)' equal to zero and attempt to solve: Simplifying 2 + x + 3xy + 6y = 0 Solving 2 + x + 3xy + 6y = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + x + 3xy + -2 + 6y = 0 + -2 Reorder the terms: 2 + -2 + x + 3xy + 6y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x + 3xy + 6y = 0 + -2 x + 3xy + 6y = 0 + -2 Combine like terms: 0 + -2 = -2 x + 3xy + 6y = -2 Add '-6y' to each side of the equation. x + 3xy + 6y + -6y = -2 + -6y Combine like terms: 6y + -6y = 0 x + 3xy + 0 = -2 + -6y x + 3xy = -2 + -6y The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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