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Simplifying (y + -12)(6x + -32)(3y + -8)(2x + -20) = 0 Reorder the terms: (-12 + y)(6x + -32)(3y + -8)(2x + -20) = 0 Reorder the terms: (-12 + y)(-32 + 6x)(3y + -8)(2x + -20) = 0 Reorder the terms: (-12 + y)(-32 + 6x)(-8 + 3y)(2x + -20) = 0 Reorder the terms: (-12 + y)(-32 + 6x)(-8 + 3y)(-20 + 2x) = 0 Multiply (-12 + y) * (-32 + 6x) (-12(-32 + 6x) + y(-32 + 6x))(-8 + 3y)(-20 + 2x) = 0 ((-32 * -12 + 6x * -12) + y(-32 + 6x))(-8 + 3y)(-20 + 2x) = 0 ((384 + -72x) + y(-32 + 6x))(-8 + 3y)(-20 + 2x) = 0 (384 + -72x + (-32 * y + 6x * y))(-8 + 3y)(-20 + 2x) = 0 Reorder the terms: (384 + -72x + (6xy + -32y))(-8 + 3y)(-20 + 2x) = 0 (384 + -72x + (6xy + -32y))(-8 + 3y)(-20 + 2x) = 0 (384 + -72x + 6xy + -32y)(-8 + 3y)(-20 + 2x) = 0 Multiply (384 + -72x + 6xy + -32y) * (-8 + 3y) (384(-8 + 3y) + -72x * (-8 + 3y) + 6xy * (-8 + 3y) + -32y * (-8 + 3y))(-20 + 2x) = 0 ((-8 * 384 + 3y * 384) + -72x * (-8 + 3y) + 6xy * (-8 + 3y) + -32y * (-8 + 3y))(-20 + 2x) = 0 ((-3072 + 1152y) + -72x * (-8 + 3y) + 6xy * (-8 + 3y) + -32y * (-8 + 3y))(-20 + 2x) = 0 (-3072 + 1152y + (-8 * -72x + 3y * -72x) + 6xy * (-8 + 3y) + -32y * (-8 + 3y))(-20 + 2x) = 0 (-3072 + 1152y + (576x + -216xy) + 6xy * (-8 + 3y) + -32y * (-8 + 3y))(-20 + 2x) = 0 (-3072 + 1152y + 576x + -216xy + (-8 * 6xy + 3y * 6xy) + -32y * (-8 + 3y))(-20 + 2x) = 0 (-3072 + 1152y + 576x + -216xy + (-48xy + 18xy2) + -32y * (-8 + 3y))(-20 + 2x) = 0 (-3072 + 1152y + 576x + -216xy + -48xy + 18xy2 + (-8 * -32y + 3y * -32y))(-20 + 2x) = 0 (-3072 + 1152y + 576x + -216xy + -48xy + 18xy2 + (256y + -96y2))(-20 + 2x) = 0 Reorder the terms: (-3072 + 576x + -216xy + -48xy + 18xy2 + 1152y + 256y + -96y2)(-20 + 2x) = 0 Combine like terms: -216xy + -48xy = -264xy (-3072 + 576x + -264xy + 18xy2 + 1152y + 256y + -96y2)(-20 + 2x) = 0 Combine like terms: 1152y + 256y = 1408y (-3072 + 576x + -264xy + 18xy2 + 1408y + -96y2)(-20 + 2x) = 0 Multiply (-3072 + 576x + -264xy + 18xy2 + 1408y + -96y2) * (-20 + 2x) (-3072(-20 + 2x) + 576x * (-20 + 2x) + -264xy * (-20 + 2x) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 ((-20 * -3072 + 2x * -3072) + 576x * (-20 + 2x) + -264xy * (-20 + 2x) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 ((61440 + -6144x) + 576x * (-20 + 2x) + -264xy * (-20 + 2x) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + (-20 * 576x + 2x * 576x) + -264xy * (-20 + 2x) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + (-11520x + 1152x2) + -264xy * (-20 + 2x) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + (-20 * -264xy + 2x * -264xy) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + (5280xy + -528x2y) + 18xy2 * (-20 + 2x) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + (-20 * 18xy2 + 2x * 18xy2) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + (-360xy2 + 36x2y2) + 1408y * (-20 + 2x) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + (-20 * 1408y + 2x * 1408y) + -96y2 * (-20 + 2x)) = 0 Reorder the terms: (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + (2816xy + -28160y) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + (2816xy + -28160y) + -96y2 * (-20 + 2x)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + 2816xy + -28160y + (-20 * -96y2 + 2x * -96y2)) = 0 Reorder the terms: (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + 2816xy + -28160y + (-192xy2 + 1920y2)) = 0 (61440 + -6144x + -11520x + 1152x2 + 5280xy + -528x2y + -360xy2 + 36x2y2 + 2816xy + -28160y + (-192xy2 + 1920y2)) = 0 Reorder the terms: (61440 + -6144x + -11520x + 5280xy + 2816xy + -360xy2 + -192xy2 + 1152x2 + -528x2y + 36x2y2 + -28160y + 1920y2) = 0 Combine like terms: -6144x + -11520x = -17664x (61440 + -17664x + 5280xy + 2816xy + -360xy2 + -192xy2 + 1152x2 + -528x2y + 36x2y2 + -28160y + 1920y2) = 0 Combine like terms: 5280xy + 2816xy = 8096xy (61440 + -17664x + 8096xy + -360xy2 + -192xy2 + 1152x2 + -528x2y + 36x2y2 + -28160y + 1920y2) = 0 Combine like terms: -360xy2 + -192xy2 = -552xy2 (61440 + -17664x + 8096xy + -552xy2 + 1152x2 + -528x2y + 36x2y2 + -28160y + 1920y2) = 0 Solving 61440 + -17664x + 8096xy + -552xy2 + 1152x2 + -528x2y + 36x2y2 + -28160y + 1920y2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(15360 + -4416x + 2024xy + -138xy2 + 288x2 + -132x2y + 9x2y2 + -7040y + 480y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(15360 + -4416x + 2024xy + -138xy2 + 288x2 + -132x2y + 9x2y2 + -7040y + 480y2)' equal to zero and attempt to solve: Simplifying 15360 + -4416x + 2024xy + -138xy2 + 288x2 + -132x2y + 9x2y2 + -7040y + 480y2 = 0 Solving 15360 + -4416x + 2024xy + -138xy2 + 288x2 + -132x2y + 9x2y2 + -7040y + 480y2 = 0 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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