3x^2+14ux+8u^2=0

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Solution for 3x^2+14ux+8u^2=0 equation: 


Simplifying
3x2 + 14ux + 8u2 = 0

Reorder the terms:
14ux + 8u2 + 3x2 = 0

Solving
14ux + 8u2 + 3x2 = 0

Solving for variable 'u'.

Factor a trinomial.
(4u + x)(2u + 3x) = 0


Subproblem 1
Set the factor '(4u + x)' equal to zero and attempt to solve:

Simplifying
4u + x = 0

Solving
4u + x = 0

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

Add '-1x' to each side of the equation.
4u + x + -1x = 0 + -1x

Combine like terms: x + -1x = 0
4u + 0 = 0 + -1x
4u = 0 + -1x
Remove the zero:
4u = -1x

Divide each side by '4'.
u = -0.25x

Simplifying
u = -0.25x

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

Simplifying
2u + 3x = 0

Solving
2u + 3x = 0

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

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

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

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

Simplifying
u = -1.5x
Solution
u = {-0.25x, -1.5x}

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