(4v^2-6v+7)=-(-v^2+3v+5)

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Solution for (4v^2-6v+7)=-(-v^2+3v+5) equation: 


Simplifying
(4v2 + -6v + 7) = -1(-1v2 + 3v + 5)

Reorder the terms:
(7 + -6v + 4v2) = -1(-1v2 + 3v + 5)

Remove parenthesis around (7 + -6v + 4v2)
7 + -6v + 4v2 = -1(-1v2 + 3v + 5)

Reorder the terms:
7 + -6v + 4v2 = -1(5 + 3v + -1v2)
7 + -6v + 4v2 = (5 * -1 + 3v * -1 + -1v2 * -1)
7 + -6v + 4v2 = (-5 + -3v + 1v2)

Solving
7 + -6v + 4v2 = -5 + -3v + 1v2

Solving for variable 'v'.

Reorder the terms:
7 + 5 + -6v + 3v + 4v2 + -1v2 = -5 + -3v + 1v2 + 5 + 3v + -1v2

Combine like terms: 7 + 5 = 12
12 + -6v + 3v + 4v2 + -1v2 = -5 + -3v + 1v2 + 5 + 3v + -1v2

Combine like terms: -6v + 3v = -3v
12 + -3v + 4v2 + -1v2 = -5 + -3v + 1v2 + 5 + 3v + -1v2

Combine like terms: 4v2 + -1v2 = 3v2
12 + -3v + 3v2 = -5 + -3v + 1v2 + 5 + 3v + -1v2

Reorder the terms:
12 + -3v + 3v2 = -5 + 5 + -3v + 3v + 1v2 + -1v2

Combine like terms: -5 + 5 = 0
12 + -3v + 3v2 = 0 + -3v + 3v + 1v2 + -1v2
12 + -3v + 3v2 = -3v + 3v + 1v2 + -1v2

Combine like terms: -3v + 3v = 0
12 + -3v + 3v2 = 0 + 1v2 + -1v2
12 + -3v + 3v2 = 1v2 + -1v2

Combine like terms: 1v2 + -1v2 = 0
12 + -3v + 3v2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + -1v + v2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -1v + v2)' equal to zero and attempt to solve:

Simplifying
4 + -1v + v2 = 0

Solving
4 + -1v + v2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -1v + -4 + v2 = 0 + -4

Reorder the terms:
4 + -4 + -1v + v2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v + v2 = 0 + -4
-1v + v2 = 0 + -4

Combine like terms: 0 + -4 = -4
-1v + v2 = -4

The v term is -1v.  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.
-1v + 0.25 + v2 = -4 + 0.25

Reorder the terms:
0.25 + -1v + v2 = -4 + 0.25

Combine like terms: -4 + 0.25 = -3.75
0.25 + -1v + v2 = -3.75

Factor a perfect square on the left side:
(v + -0.5)(v + -0.5) = -3.75

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.

The solution to this equation could not be determined.

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