6(v-3)v=-14

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Solution for 6(v-3)v=-14 equation: 


Simplifying
6(v + -3) * v = -14

Reorder the terms:
6(-3 + v) * v = -14

Reorder the terms for easier multiplication:
6v(-3 + v) = -14
(-3 * 6v + v * 6v) = -14
(-18v + 6v2) = -14

Solving
-18v + 6v2 = -14

Solving for variable 'v'.

Reorder the terms:
14 + -18v + 6v2 = -14 + 14

Combine like terms: -14 + 14 = 0
14 + -18v + 6v2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -9v + 3v2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -9v + 3v2)' equal to zero and attempt to solve:

Simplifying
7 + -9v + 3v2 = 0

Solving
7 + -9v + 3v2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
2.333333333 + -3v + v2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -3v + -2.333333333 + v2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -3v + v2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -3v + v2 = 0 + -2.333333333
-3v + v2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-3v + v2 = -2.333333333

The v term is -3v.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3v + 2.25 + v2 = -2.333333333 + 2.25

Reorder the terms:
2.25 + -3v + v2 = -2.333333333 + 2.25

Combine like terms: -2.333333333 + 2.25 = -0.083333333
2.25 + -3v + v2 = -0.083333333

Factor a perfect square on the left side:
(v + -1.5)(v + -1.5) = -0.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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