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Simplifying 2y + 3(2x + 4z) + -4(z + -2y) * 12x = 0 2y + (2x * 3 + 4z * 3) + -4(z + -2y) * 12x = 0 2y + (6x + 12z) + -4(z + -2y) * 12x = 0 Reorder the terms: 2y + 6x + 12z + -4(-2y + z) * 12x = 0 Reorder the terms for easier multiplication: 2y + 6x + 12z + -4 * 12x(-2y + z) = 0 Multiply -4 * 12 2y + 6x + 12z + -48x(-2y + z) = 0 2y + 6x + 12z + (-2y * -48x + z * -48x) = 0 2y + 6x + 12z + (96xy + -48xz) = 0 Reorder the terms: 6x + 96xy + -48xz + 2y + 12z = 0 Solving 6x + 96xy + -48xz + 2y + 12z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2y' to each side of the equation. 6x + 96xy + -48xz + 2y + -2y + 12z = 0 + -2y Combine like terms: 2y + -2y = 0 6x + 96xy + -48xz + 0 + 12z = 0 + -2y 6x + 96xy + -48xz + 12z = 0 + -2y Remove the zero: 6x + 96xy + -48xz + 12z = -2y Add '-12z' to each side of the equation. 6x + 96xy + -48xz + 12z + -12z = -2y + -12z Combine like terms: 12z + -12z = 0 6x + 96xy + -48xz + 0 = -2y + -12z 6x + 96xy + -48xz = -2y + -12z Reorder the terms: 6x + 96xy + -48xz + 2y + 12z = -2y + 2y + -12z + 12z Combine like terms: -2y + 2y = 0 6x + 96xy + -48xz + 2y + 12z = 0 + -12z + 12z 6x + 96xy + -48xz + 2y + 12z = -12z + 12z Combine like terms: -12z + 12z = 0 6x + 96xy + -48xz + 2y + 12z = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3x + 48xy + -24xz + y + 6z) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3x + 48xy + -24xz + y + 6z)' equal to zero and attempt to solve: Simplifying 3x + 48xy + -24xz + y + 6z = 0 Solving 3x + 48xy + -24xz + y + 6z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 3x + 48xy + -24xz + y + -1y + 6z = 0 + -1y Combine like terms: y + -1y = 0 3x + 48xy + -24xz + 0 + 6z = 0 + -1y 3x + 48xy + -24xz + 6z = 0 + -1y Remove the zero: 3x + 48xy + -24xz + 6z = -1y Add '-6z' to each side of the equation. 3x + 48xy + -24xz + 6z + -6z = -1y + -6z Combine like terms: 6z + -6z = 0 3x + 48xy + -24xz + 0 = -1y + -6z 3x + 48xy + -24xz = -1y + -6z 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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