3a^2+51a+216a=0

Solution for 3a^2+51a+216a=0 equation:

Simplifying
3a2 + 51a + 216a = 0

Reorder the terms:
51a + 216a + 3a2 = 0

Combine like terms: 51a + 216a = 267a
267a + 3a2 = 0

Solving
267a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(89 + a) = 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 '(89 + a)' equal to zero and attempt to solve:

Simplifying
89 + a = 0

Solving
89 + a = 0

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

Add '-89' to each side of the equation.
89 + -89 + a = 0 + -89

Combine like terms: 89 + -89 = 0
0 + a = 0 + -89
a = 0 + -89

Combine like terms: 0 + -89 = -89
a = -89

Simplifying
a = -89
Solution
a = {0, -89}