3v(v^2-7v+19)=0

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Solution for 3v(v^2-7v+19)=0 equation: 


Simplifying
3v(v2 + -7v + 19) = 0

Reorder the terms:
3v(19 + -7v + v2) = 0
(19 * 3v + -7v * 3v + v2 * 3v) = 0
(57v + -21v2 + 3v3) = 0

Solving
57v + -21v2 + 3v3 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '3v'.
3v(19 + -7v + v2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'v' equal to zero and attempt to solve:

Simplifying
v = 0

Solving
v = 0

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

Simplifying
v = 0

Subproblem 2
Set the factor '(19 + -7v + v2)' equal to zero and attempt to solve:

Simplifying
19 + -7v + v2 = 0

Solving
19 + -7v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -7v + -19 + v2 = 0 + -19

Reorder the terms:
19 + -19 + -7v + v2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -7v + v2 = 0 + -19
-7v + v2 = 0 + -19

Combine like terms: 0 + -19 = -19
-7v + v2 = -19

The v term is -7v.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7v + 12.25 + v2 = -19 + 12.25

Reorder the terms:
12.25 + -7v + v2 = -19 + 12.25

Combine like terms: -19 + 12.25 = -6.75
12.25 + -7v + v2 = -6.75

Factor a perfect square on the left side:
(v + -3.5)(v + -3.5) = -6.75

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.
Solution
v = {0}

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