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Simplifying (3x + -6)(y + -6) = 420 Reorder the terms: (-6 + 3x)(y + -6) = 420 Reorder the terms: (-6 + 3x)(-6 + y) = 420 Multiply (-6 + 3x) * (-6 + y) (-6(-6 + y) + 3x * (-6 + y)) = 420 ((-6 * -6 + y * -6) + 3x * (-6 + y)) = 420 ((36 + -6y) + 3x * (-6 + y)) = 420 (36 + -6y + (-6 * 3x + y * 3x)) = 420 (36 + -6y + (-18x + 3xy)) = 420 Reorder the terms: (36 + -18x + 3xy + -6y) = 420 (36 + -18x + 3xy + -6y) = 420 Solving 36 + -18x + 3xy + -6y = 420 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-36' to each side of the equation. 36 + -18x + 3xy + -36 + -6y = 420 + -36 Reorder the terms: 36 + -36 + -18x + 3xy + -6y = 420 + -36 Combine like terms: 36 + -36 = 0 0 + -18x + 3xy + -6y = 420 + -36 -18x + 3xy + -6y = 420 + -36 Combine like terms: 420 + -36 = 384 -18x + 3xy + -6y = 384 Add '6y' to each side of the equation. -18x + 3xy + -6y + 6y = 384 + 6y Combine like terms: -6y + 6y = 0 -18x + 3xy + 0 = 384 + 6y -18x + 3xy = 384 + 6y Reorder the terms: -384 + -18x + 3xy + -6y = 384 + 6y + -384 + -6y Reorder the terms: -384 + -18x + 3xy + -6y = 384 + -384 + 6y + -6y Combine like terms: 384 + -384 = 0 -384 + -18x + 3xy + -6y = 0 + 6y + -6y -384 + -18x + 3xy + -6y = 6y + -6y Combine like terms: 6y + -6y = 0 -384 + -18x + 3xy + -6y = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-128 + -6x + xy + -2y) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-128 + -6x + xy + -2y)' equal to zero and attempt to solve: Simplifying -128 + -6x + xy + -2y = 0 Solving -128 + -6x + xy + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '128' to each side of the equation. -128 + -6x + xy + 128 + -2y = 0 + 128 Reorder the terms: -128 + 128 + -6x + xy + -2y = 0 + 128 Combine like terms: -128 + 128 = 0 0 + -6x + xy + -2y = 0 + 128 -6x + xy + -2y = 0 + 128 Combine like terms: 0 + 128 = 128 -6x + xy + -2y = 128 Add '2y' to each side of the equation. -6x + xy + -2y + 2y = 128 + 2y Combine like terms: -2y + 2y = 0 -6x + xy + 0 = 128 + 2y -6x + xy = 128 + 2y 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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