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Simplifying 4(x + 3) * y2 + 54(x + 3) * y + -90(x + 3) = 0 Reorder the terms: 4(3 + x) * y2 + 54(x + 3) * y + -90(x + 3) = 0 Reorder the terms for easier multiplication: 4y2(3 + x) + 54(x + 3) * y + -90(x + 3) = 0 (3 * 4y2 + x * 4y2) + 54(x + 3) * y + -90(x + 3) = 0 Reorder the terms: (4xy2 + 12y2) + 54(x + 3) * y + -90(x + 3) = 0 (4xy2 + 12y2) + 54(x + 3) * y + -90(x + 3) = 0 Reorder the terms: 4xy2 + 12y2 + 54(3 + x) * y + -90(x + 3) = 0 Reorder the terms for easier multiplication: 4xy2 + 12y2 + 54y(3 + x) + -90(x + 3) = 0 4xy2 + 12y2 + (3 * 54y + x * 54y) + -90(x + 3) = 0 Reorder the terms: 4xy2 + 12y2 + (54xy + 162y) + -90(x + 3) = 0 4xy2 + 12y2 + (54xy + 162y) + -90(x + 3) = 0 Reorder the terms: 4xy2 + 12y2 + 54xy + 162y + -90(3 + x) = 0 4xy2 + 12y2 + 54xy + 162y + (3 * -90 + x * -90) = 0 4xy2 + 12y2 + 54xy + 162y + (-270 + -90x) = 0 Reorder the terms: -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 Solving -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '270' to each side of the equation. -270 + -90x + 54xy + 4xy2 + 162y + 270 + 12y2 = 0 + 270 Reorder the terms: -270 + 270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 + 270 -90x + 54xy + 4xy2 + 162y + 12y2 = 0 + 270 Combine like terms: 0 + 270 = 270 -90x + 54xy + 4xy2 + 162y + 12y2 = 270 Add '-162y' to each side of the equation. -90x + 54xy + 4xy2 + 162y + -162y + 12y2 = 270 + -162y Combine like terms: 162y + -162y = 0 -90x + 54xy + 4xy2 + 0 + 12y2 = 270 + -162y -90x + 54xy + 4xy2 + 12y2 = 270 + -162y Add '-12y2' to each side of the equation. -90x + 54xy + 4xy2 + 12y2 + -12y2 = 270 + -162y + -12y2 Combine like terms: 12y2 + -12y2 = 0 -90x + 54xy + 4xy2 + 0 = 270 + -162y + -12y2 -90x + 54xy + 4xy2 = 270 + -162y + -12y2 Reorder the terms: -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 270 + -162y + -12y2 + -270 + 162y + 12y2 Reorder the terms: -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 270 + -270 + -162y + 162y + -12y2 + 12y2 Combine like terms: 270 + -270 = 0 -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 + -162y + 162y + -12y2 + 12y2 -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = -162y + 162y + -12y2 + 12y2 Combine like terms: -162y + 162y = 0 -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 + -12y2 + 12y2 -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = -12y2 + 12y2 Combine like terms: -12y2 + 12y2 = 0 -270 + -90x + 54xy + 4xy2 + 162y + 12y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-135 + -45x + 27xy + 2xy2 + 81y + 6y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-135 + -45x + 27xy + 2xy2 + 81y + 6y2)' equal to zero and attempt to solve: Simplifying -135 + -45x + 27xy + 2xy2 + 81y + 6y2 = 0 Solving -135 + -45x + 27xy + 2xy2 + 81y + 6y2 = 0 Move all terms containing x to the left, all other terms to the right. Add '135' to each side of the equation. -135 + -45x + 27xy + 2xy2 + 81y + 135 + 6y2 = 0 + 135 Reorder the terms: -135 + 135 + -45x + 27xy + 2xy2 + 81y + 6y2 = 0 + 135 Combine like terms: -135 + 135 = 0 0 + -45x + 27xy + 2xy2 + 81y + 6y2 = 0 + 135 -45x + 27xy + 2xy2 + 81y + 6y2 = 0 + 135 Combine like terms: 0 + 135 = 135 -45x + 27xy + 2xy2 + 81y + 6y2 = 135 Add '-81y' to each side of the equation. -45x + 27xy + 2xy2 + 81y + -81y + 6y2 = 135 + -81y Combine like terms: 81y + -81y = 0 -45x + 27xy + 2xy2 + 0 + 6y2 = 135 + -81y -45x + 27xy + 2xy2 + 6y2 = 135 + -81y Add '-6y2' to each side of the equation. -45x + 27xy + 2xy2 + 6y2 + -6y2 = 135 + -81y + -6y2 Combine like terms: 6y2 + -6y2 = 0 -45x + 27xy + 2xy2 + 0 = 135 + -81y + -6y2 -45x + 27xy + 2xy2 = 135 + -81y + -6y2 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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