(9x^3+x^2)(-81x-9)=0

Solution for (9x^3+x^2)(-81x-9)=0 equation:

Simplifying
(9x3 + x2)(-81x + -9) = 0

Reorder the terms:
(x2 + 9x3)(-81x + -9) = 0

Reorder the terms:
(x2 + 9x3)(-9 + -81x) = 0

Multiply (x2 + 9x3) * (-9 + -81x)
(x2(-9 + -81x) + 9x3 * (-9 + -81x)) = 0
((-9 * x2 + -81x * x2) + 9x3 * (-9 + -81x)) = 0
((-9x2 + -81x3) + 9x3 * (-9 + -81x)) = 0
(-9x2 + -81x3 + (-9 * 9x3 + -81x * 9x3)) = 0
(-9x2 + -81x3 + (-81x3 + -729x4)) = 0

Combine like terms: -81x3 + -81x3 = -162x3
(-9x2 + -162x3 + -729x4) = 0

Solving
-9x2 + -162x3 + -729x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-9x2'.
-9x2(1 + 18x + 81x2) = 0

Factor a trinomial.
-9x2((1 + 9x)(1 + 9x)) = 0

Ignore the factor -9.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Subproblem 3
Set the factor '(1 + 9x)' equal to zero and attempt to solve:

Simplifying
1 + 9x = 0

Solving
1 + 9x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 9x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 9x = 0 + -1
9x = 0 + -1

Combine like terms: 0 + -1 = -1
9x = -1

Divide each side by '9'.
x = -0.1111111111

Simplifying
x = -0.1111111111
Solution
x = {0, -0.1111111111, -0.1111111111}