a(x+6)(x^2-18x+82)=0

Solution for a(x+6)(x^2-18x+82)=0 equation:

Simplifying
a(x + 6)(x2 + -18x + 82) = 0

Reorder the terms:
a(6 + x)(x2 + -18x + 82) = 0

Reorder the terms:
a(6 + x)(82 + -18x + x2) = 0

Multiply (6 + x) * (82 + -18x + x2)
a(6(82 + -18x + x2) + x(82 + -18x + x2)) = 0
a((82 * 6 + -18x * 6 + x2 * 6) + x(82 + -18x + x2)) = 0
a((492 + -108x + 6x2) + x(82 + -18x + x2)) = 0
a(492 + -108x + 6x2 + (82 * x + -18x * x + x2 * x)) = 0
a(492 + -108x + 6x2 + (82x + -18x2 + x3)) = 0

Reorder the terms:
a(492 + -108x + 82x + 6x2 + -18x2 + x3) = 0

Combine like terms: -108x + 82x = -26x
a(492 + -26x + 6x2 + -18x2 + x3) = 0

Combine like terms: 6x2 + -18x2 = -12x2
a(492 + -26x + -12x2 + x3) = 0
(492 * a + -26x * a + -12x2 * a + x3 * a) = 0
(492a + -26ax + -12ax2 + ax3) = 0

Solving
492a + -26ax + -12ax2 + ax3 = 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(492 + -26x + -12x2 + x3) = 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 '(492 + -26x + -12x2 + x3)' equal to zero and attempt to solve:

Simplifying
492 + -26x + -12x2 + x3 = 0

Solving
492 + -26x + -12x2 + x3 = 0

Move all terms containing a to the left, all other terms to the right.

Add '-492' to each side of the equation.
492 + -26x + -12x2 + -492 + x3 = 0 + -492

Reorder the terms:
492 + -492 + -26x + -12x2 + x3 = 0 + -492

Combine like terms: 492 + -492 = 0
0 + -26x + -12x2 + x3 = 0 + -492
-26x + -12x2 + x3 = 0 + -492

Combine like terms: 0 + -492 = -492
-26x + -12x2 + x3 = -492

Add '26x' to each side of the equation.
-26x + -12x2 + 26x + x3 = -492 + 26x

Reorder the terms:
-26x + 26x + -12x2 + x3 = -492 + 26x

Combine like terms: -26x + 26x = 0
0 + -12x2 + x3 = -492 + 26x
-12x2 + x3 = -492 + 26x

Add '12x2' to each side of the equation.
-12x2 + 12x2 + x3 = -492 + 26x + 12x2

Combine like terms: -12x2 + 12x2 = 0
0 + x3 = -492 + 26x + 12x2
x3 = -492 + 26x + 12x2

Add '-1x3' to each side of the equation.
x3 + -1x3 = -492 + 26x + 12x2 + -1x3

Combine like terms: x3 + -1x3 = 0
0 = -492 + 26x + 12x2 + -1x3

Simplifying
0 = -492 + 26x + 12x2 + -1x3

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}