x^2+5ax+6a^2=

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Solution for x^2+5ax+6a^2= equation: 


Simplifying
x2 + 5ax + 6a2 = 0

Reorder the terms:
5ax + 6a2 + x2 = 0

Solving
5ax + 6a2 + x2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + x)(2a + x) = 0


Subproblem 1
Set the factor '(3a + x)' equal to zero and attempt to solve:

Simplifying
3a + x = 0

Solving
3a + x = 0

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

Add '-1x' to each side of the equation.
3a + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
3a + 0 = 0 + -1x
3a = 0 + -1x
Remove the zero:
3a = -1x

Divide each side by '3'.
a = -0.3333333333x

Simplifying
a = -0.3333333333x

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

Simplifying
2a + x = 0

Solving
2a + x = 0

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

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

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

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

Simplifying
a = -0.5x
Solution
a = {-0.3333333333x, -0.5x}

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