c^2+3ac+2a^2=0

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Solution for c^2+3ac+2a^2=0 equation: 


Simplifying
c2 + 3ac + 2a2 = 0

Reorder the terms:
3ac + 2a2 + c2 = 0

Solving
3ac + 2a2 + c2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + c)(a + c) = 0


Subproblem 1
Set the factor '(2a + c)' equal to zero and attempt to solve:

Simplifying
2a + c = 0

Solving
2a + c = 0

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

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

Combine like terms: c + -1c = 0
2a + 0 = 0 + -1c
2a = 0 + -1c
Remove the zero:
2a = -1c

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

Simplifying
a = -0.5c

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

Simplifying
a + c = 0

Solving
a + c = 0

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

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

Combine like terms: c + -1c = 0
a + 0 = 0 + -1c
a = 0 + -1c
Remove the zero:
a = -1c

Simplifying
a = -1c
Solution
a = {-0.5c, -1c}

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