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Simplifying ax + 2x + 2ax + 4x + ax2 + 2x2 = 0 Reorder the terms: ax + 2ax + ax2 + 2x + 4x + 2x2 = 0 Combine like terms: ax + 2ax = 3ax 3ax + ax2 + 2x + 4x + 2x2 = 0 Combine like terms: 2x + 4x = 6x 3ax + ax2 + 6x + 2x2 = 0 Solving 3ax + ax2 + 6x + 2x2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6x' to each side of the equation. 3ax + ax2 + 6x + -6x + 2x2 = 0 + -6x Combine like terms: 6x + -6x = 0 3ax + ax2 + 0 + 2x2 = 0 + -6x 3ax + ax2 + 2x2 = 0 + -6x Remove the zero: 3ax + ax2 + 2x2 = -6x Add '-2x2' to each side of the equation. 3ax + ax2 + 2x2 + -2x2 = -6x + -2x2 Combine like terms: 2x2 + -2x2 = 0 3ax + ax2 + 0 = -6x + -2x2 3ax + ax2 = -6x + -2x2 Reorder the terms: 3ax + ax2 + 6x + 2x2 = -6x + 6x + -2x2 + 2x2 Combine like terms: -6x + 6x = 0 3ax + ax2 + 6x + 2x2 = 0 + -2x2 + 2x2 3ax + ax2 + 6x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 3ax + ax2 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3a + ax + 6 + 2x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(3a + ax + 6 + 2x)' equal to zero and attempt to solve: Simplifying 3a + ax + 6 + 2x = 0 Reorder the terms: 6 + 3a + ax + 2x = 0 Solving 6 + 3a + ax + 2x = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 3a + ax + -6 + 2x = 0 + -6 Reorder the terms: 6 + -6 + 3a + ax + 2x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 3a + ax + 2x = 0 + -6 3a + ax + 2x = 0 + -6 Combine like terms: 0 + -6 = -6 3a + ax + 2x = -6 Add '-2x' to each side of the equation. 3a + ax + 2x + -2x = -6 + -2x Combine like terms: 2x + -2x = 0 3a + ax + 0 = -6 + -2x 3a + ax = -6 + -2x 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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