21v^2+21v+54=0

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Solution for 21v^2+21v+54=0 equation: 


Simplifying
21v2 + 21v + 54 = 0

Reorder the terms:
54 + 21v + 21v2 = 0

Solving
54 + 21v + 21v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 7v + 7v2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + 7v + 7v2)' equal to zero and attempt to solve:

Simplifying
18 + 7v + 7v2 = 0

Solving
18 + 7v + 7v2 = 0

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

Divide each side by '7'.
2.571428571 + v + v2 = 0

Move the constant term to the right:

Add '-2.571428571' to each side of the equation.
2.571428571 + v + -2.571428571 + v2 = 0 + -2.571428571

Reorder the terms:
2.571428571 + -2.571428571 + v + v2 = 0 + -2.571428571

Combine like terms: 2.571428571 + -2.571428571 = 0.000000000
0.000000000 + v + v2 = 0 + -2.571428571
v + v2 = 0 + -2.571428571

Combine like terms: 0 + -2.571428571 = -2.571428571
v + v2 = -2.571428571

The v term is v.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + v2 = -2.571428571 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + v2 = -2.571428571 + 0.25

Combine like terms: -2.571428571 + 0.25 = -2.321428571
1.25 + v2 = -2.321428571

Factor a perfect square on the left side:
(v + 0.5)(v + 0.5) = -2.321428571

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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