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Simplifying 6(x + 1) * y2 + 81(x + 1) * y + -135(x + 1) = 0 Reorder the terms: 6(1 + x) * y2 + 81(x + 1) * y + -135(x + 1) = 0 Reorder the terms for easier multiplication: 6y2(1 + x) + 81(x + 1) * y + -135(x + 1) = 0 (1 * 6y2 + x * 6y2) + 81(x + 1) * y + -135(x + 1) = 0 Reorder the terms: (6xy2 + 6y2) + 81(x + 1) * y + -135(x + 1) = 0 (6xy2 + 6y2) + 81(x + 1) * y + -135(x + 1) = 0 Reorder the terms: 6xy2 + 6y2 + 81(1 + x) * y + -135(x + 1) = 0 Reorder the terms for easier multiplication: 6xy2 + 6y2 + 81y(1 + x) + -135(x + 1) = 0 6xy2 + 6y2 + (1 * 81y + x * 81y) + -135(x + 1) = 0 Reorder the terms: 6xy2 + 6y2 + (81xy + 81y) + -135(x + 1) = 0 6xy2 + 6y2 + (81xy + 81y) + -135(x + 1) = 0 Reorder the terms: 6xy2 + 6y2 + 81xy + 81y + -135(1 + x) = 0 6xy2 + 6y2 + 81xy + 81y + (1 * -135 + x * -135) = 0 6xy2 + 6y2 + 81xy + 81y + (-135 + -135x) = 0 Reorder the terms: -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 Solving -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '135' to each side of the equation. -135 + -135x + 81xy + 6xy2 + 81y + 135 + 6y2 = 0 + 135 Reorder the terms: -135 + 135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 + 135 -135x + 81xy + 6xy2 + 81y + 6y2 = 0 + 135 Combine like terms: 0 + 135 = 135 -135x + 81xy + 6xy2 + 81y + 6y2 = 135 Add '-81y' to each side of the equation. -135x + 81xy + 6xy2 + 81y + -81y + 6y2 = 135 + -81y Combine like terms: 81y + -81y = 0 -135x + 81xy + 6xy2 + 0 + 6y2 = 135 + -81y -135x + 81xy + 6xy2 + 6y2 = 135 + -81y Add '-6y2' to each side of the equation. -135x + 81xy + 6xy2 + 6y2 + -6y2 = 135 + -81y + -6y2 Combine like terms: 6y2 + -6y2 = 0 -135x + 81xy + 6xy2 + 0 = 135 + -81y + -6y2 -135x + 81xy + 6xy2 = 135 + -81y + -6y2 Reorder the terms: -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 135 + -81y + -6y2 + -135 + 81y + 6y2 Reorder the terms: -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 135 + -135 + -81y + 81y + -6y2 + 6y2 Combine like terms: 135 + -135 = 0 -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 + -81y + 81y + -6y2 + 6y2 -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = -81y + 81y + -6y2 + 6y2 Combine like terms: -81y + 81y = 0 -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 + -6y2 + 6y2 -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = -6y2 + 6y2 Combine like terms: -6y2 + 6y2 = 0 -135 + -135x + 81xy + 6xy2 + 81y + 6y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-45 + -45x + 27xy + 2xy2 + 27y + 2y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-45 + -45x + 27xy + 2xy2 + 27y + 2y2)' equal to zero and attempt to solve: Simplifying -45 + -45x + 27xy + 2xy2 + 27y + 2y2 = 0 Solving -45 + -45x + 27xy + 2xy2 + 27y + 2y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '45' to each side of the equation. -45 + -45x + 27xy + 2xy2 + 27y + 45 + 2y2 = 0 + 45 Reorder the terms: -45 + 45 + -45x + 27xy + 2xy2 + 27y + 2y2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + -45x + 27xy + 2xy2 + 27y + 2y2 = 0 + 45 -45x + 27xy + 2xy2 + 27y + 2y2 = 0 + 45 Combine like terms: 0 + 45 = 45 -45x + 27xy + 2xy2 + 27y + 2y2 = 45 Add '-27y' to each side of the equation. -45x + 27xy + 2xy2 + 27y + -27y + 2y2 = 45 + -27y Combine like terms: 27y + -27y = 0 -45x + 27xy + 2xy2 + 0 + 2y2 = 45 + -27y -45x + 27xy + 2xy2 + 2y2 = 45 + -27y Add '-2y2' to each side of the equation. -45x + 27xy + 2xy2 + 2y2 + -2y2 = 45 + -27y + -2y2 Combine like terms: 2y2 + -2y2 = 0 -45x + 27xy + 2xy2 + 0 = 45 + -27y + -2y2 -45x + 27xy + 2xy2 = 45 + -27y + -2y2 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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