27a^2+33ac+10c^2=0

Solution for 27a^2+33ac+10c^2=0 equation:

Simplifying
27a2 + 33ac + 10c2 = 0

Reorder the terms:
33ac + 27a2 + 10c2 = 0

Solving
33ac + 27a2 + 10c2 = 0

Solving for variable 'a'.

Factor a trinomial.
(9a + 5c)(3a + 2c) = 0

Subproblem 1
Set the factor '(9a + 5c)' equal to zero and attempt to solve:

Simplifying
9a + 5c = 0

Solving
9a + 5c = 0

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

Add '-5c' to each side of the equation.
9a + 5c + -5c = 0 + -5c

Combine like terms: 5c + -5c = 0
9a + 0 = 0 + -5c
9a = 0 + -5c
Remove the zero:
9a = -5c

Divide each side by '9'.
a = -0.5555555556c

Simplifying
a = -0.5555555556c
Subproblem 2
Set the factor '(3a + 2c)' equal to zero and attempt to solve:

Simplifying
3a + 2c = 0

Solving
3a + 2c = 0

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

Add '-2c' to each side of the equation.
3a + 2c + -2c = 0 + -2c

Combine like terms: 2c + -2c = 0
3a + 0 = 0 + -2c
3a = 0 + -2c
Remove the zero:
3a = -2c

Divide each side by '3'.
a = -0.6666666667c

Simplifying
a = -0.6666666667c
Solution
a = {-0.5555555556c, -0.6666666667c}