a(x+6)(x+2)=0

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Solution for a(x+6)(x+2)=0 equation:


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)) = 0

Subproblem 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 = 0

Subproblem 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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