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