3a(2a+9)(a+11)=0

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Solution for 3a(2a+9)(a+11)=0 equation: 


Simplifying
3a(2a + 9)(a + 11) = 0

Reorder the terms:
3a(9 + 2a)(a + 11) = 0

Reorder the terms:
3a(9 + 2a)(11 + a) = 0

Multiply (9 + 2a) * (11 + a)
3a(9(11 + a) + 2a * (11 + a)) = 0
3a((11 * 9 + a * 9) + 2a * (11 + a)) = 0
3a((99 + 9a) + 2a * (11 + a)) = 0
3a(99 + 9a + (11 * 2a + a * 2a)) = 0
3a(99 + 9a + (22a + 2a2)) = 0

Combine like terms: 9a + 22a = 31a
3a(99 + 31a + 2a2) = 0
(99 * 3a + 31a * 3a + 2a2 * 3a) = 0
(297a + 93a2 + 6a3) = 0

Solving
297a + 93a2 + 6a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(99 + 31a + 2a2) = 0

Factor a trinomial.
3a((11 + a)(9 + 2a)) = 0

Ignore the factor 3.

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 '(11 + a)' equal to zero and attempt to solve:

Simplifying
11 + a = 0

Solving
11 + a = 0

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

Add '-11' to each side of the equation.
11 + -11 + a = 0 + -11

Combine like terms: 11 + -11 = 0
0 + a = 0 + -11
a = 0 + -11

Combine like terms: 0 + -11 = -11
a = -11

Simplifying
a = -11

Subproblem 3
Set the factor '(9 + 2a)' equal to zero and attempt to solve:

Simplifying
9 + 2a = 0

Solving
9 + 2a = 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 + 2a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2a = 0 + -9
2a = 0 + -9

Combine like terms: 0 + -9 = -9
2a = -9

Divide each side by '2'.
a = -4.5

Simplifying
a = -4.5
Solution
a = {0, -11, -4.5}

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