(2x+2va)(x+3va)=0

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Solution for (2x+2va)(x+3va)=0 equation: 


Simplifying
(2x + 2va)(x + 3va) = 0

Reorder the terms:
(2av + 2x)(x + 3va) = 0

Reorder the terms:
(2av + 2x)(3av + x) = 0

Multiply (2av + 2x) * (3av + x)
(2av * (3av + x) + 2x * (3av + x)) = 0
((3av * 2av + x * 2av) + 2x * (3av + x)) = 0

Reorder the terms:
((2avx + 6a2v2) + 2x * (3av + x)) = 0
((2avx + 6a2v2) + 2x * (3av + x)) = 0
(2avx + 6a2v2 + (3av * 2x + x * 2x)) = 0
(2avx + 6a2v2 + (6avx + 2x2)) = 0

Reorder the terms:
(2avx + 6avx + 6a2v2 + 2x2) = 0

Combine like terms: 2avx + 6avx = 8avx
(8avx + 6a2v2 + 2x2) = 0

Solving
8avx + 6a2v2 + 2x2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4avx + 3a2v2 + x2) = 0

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

Ignore the factor 2.

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

Simplifying
3av + x = 0

Solving
3av + x = 0

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

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

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

Divide each side by '3v'.
a = -0.3333333333v-1x

Simplifying
a = -0.3333333333v-1x

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

Simplifying
av + x = 0

Solving
av + x = 0

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

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

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

Divide each side by 'v'.
a = -1v-1x

Simplifying
a = -1v-1x
Solution
a = {-0.3333333333v-1x, -1v-1x}

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