a(a-9)(2a+1)=0

Solution for a(a-9)(2a+1)=0 equation:

Simplifying
a(a + -9)(2a + 1) = 0

Reorder the terms:
a(-9 + a)(2a + 1) = 0

Reorder the terms:
a(-9 + a)(1 + 2a) = 0

Multiply (-9 + a) * (1 + 2a)
a(-9(1 + 2a) + a(1 + 2a)) = 0
a((1 * -9 + 2a * -9) + a(1 + 2a)) = 0
a((-9 + -18a) + a(1 + 2a)) = 0
a(-9 + -18a + (1 * a + 2a * a)) = 0
a(-9 + -18a + (1a + 2a2)) = 0

Combine like terms: -18a + 1a = -17a
a(-9 + -17a + 2a2) = 0
(-9 * a + -17a * a + 2a2 * a) = 0
(-9a + -17a2 + 2a3) = 0

Solving
-9a + -17a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-9 + -17a + 2a2) = 0

Factor a trinomial.
a((-1 + -2a)(9 + -1a)) = 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 '(-1 + -2a)' equal to zero and attempt to solve:

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 0

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

Add '1' to each side of the equation.
-1 + 1 + -2a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2a = 0 + 1
-2a = 0 + 1

Combine like terms: 0 + 1 = 1
-2a = 1

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 3
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {0, -0.5, 9}