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Simplifying a(x + 6)(x + 2) = 0 Reorder the terms: a(6 + x)(x + 2) = 0 Reorder the terms: a(6 + x)(2 + x) = 0 Multiply (6 + x) * (2 + x) a(6(2 + x) + x(2 + x)) = 0 a((2 * 6 + x * 6) + x(2 + x)) = 0 a((12 + 6x) + x(2 + x)) = 0 a(12 + 6x + (2 * x + x * x)) = 0 a(12 + 6x + (2x + x2)) = 0 Combine like terms: 6x + 2x = 8x a(12 + 8x + x2) = 0 (12 * a + 8x * a + x2 * a) = 0 (12a + 8ax + ax2) = 0 Solving 12a + 8ax + ax2 = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'a'. a(12 + 8x + x2) = 0 Factor a trinomial. a((6 + x)(2 + x)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Add '-1x' to each side of the equation. x + -1x = -6 + -1x Combine like terms: x + -1x = 0 0 = -6 + -1x Simplifying 0 = -6 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + 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 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Add '-1x' to each side of the equation. x + -1x = -2 + -1x Combine like terms: x + -1x = 0 0 = -2 + -1x Simplifying 0 = -2 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
a = {0}
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