3x^2+8ax+4a^2=0

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Solution for 3x^2+8ax+4a^2=0 equation: 


Simplifying
3x2 + 8ax + 4a2 = 0

Reorder the terms:
8ax + 4a2 + 3x2 = 0

Solving
8ax + 4a2 + 3x2 = 0

Solving for variable 'a'.

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


Subproblem 1
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

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

Simplifying
2a + 3x = 0

Solving
2a + 3x = 0

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

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

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

Divide each side by '2'.
a = -1.5x

Simplifying
a = -1.5x
Solution
a = {-0.5x, -1.5x}

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