(2v-4)(2v-4)+6v-3=4v+4v-(3v-1)

Solution for (2v-4)(2v-4)+6v-3=4v+4v-(3v-1) equation:

Simplifying
(2v + -4)(2v + -4) + 6v + -3 = 4v + 4v + -1(3v + -1)

Reorder the terms:
(-4 + 2v)(2v + -4) + 6v + -3 = 4v + 4v + -1(3v + -1)

Reorder the terms:
(-4 + 2v)(-4 + 2v) + 6v + -3 = 4v + 4v + -1(3v + -1)

Multiply (-4 + 2v) * (-4 + 2v)
(-4(-4 + 2v) + 2v * (-4 + 2v)) + 6v + -3 = 4v + 4v + -1(3v + -1)
((-4 * -4 + 2v * -4) + 2v * (-4 + 2v)) + 6v + -3 = 4v + 4v + -1(3v + -1)
((16 + -8v) + 2v * (-4 + 2v)) + 6v + -3 = 4v + 4v + -1(3v + -1)
(16 + -8v + (-4 * 2v + 2v * 2v)) + 6v + -3 = 4v + 4v + -1(3v + -1)
(16 + -8v + (-8v + 4v2)) + 6v + -3 = 4v + 4v + -1(3v + -1)

Combine like terms: -8v + -8v = -16v
(16 + -16v + 4v2) + 6v + -3 = 4v + 4v + -1(3v + -1)

Reorder the terms:
16 + -3 + -16v + 6v + 4v2 = 4v + 4v + -1(3v + -1)

Combine like terms: 16 + -3 = 13
13 + -16v + 6v + 4v2 = 4v + 4v + -1(3v + -1)

Combine like terms: -16v + 6v = -10v
13 + -10v + 4v2 = 4v + 4v + -1(3v + -1)

Reorder the terms:
13 + -10v + 4v2 = 4v + 4v + -1(-1 + 3v)
13 + -10v + 4v2 = 4v + 4v + (-1 * -1 + 3v * -1)
13 + -10v + 4v2 = 4v + 4v + (1 + -3v)

Reorder the terms:
13 + -10v + 4v2 = 1 + 4v + 4v + -3v

Combine like terms: 4v + 4v = 8v
13 + -10v + 4v2 = 1 + 8v + -3v

Combine like terms: 8v + -3v = 5v
13 + -10v + 4v2 = 1 + 5v

Solving
13 + -10v + 4v2 = 1 + 5v

Solving for variable 'v'.

Reorder the terms:
13 + -1 + -10v + -5v + 4v2 = 1 + 5v + -1 + -5v

Combine like terms: 13 + -1 = 12
12 + -10v + -5v + 4v2 = 1 + 5v + -1 + -5v

Combine like terms: -10v + -5v = -15v
12 + -15v + 4v2 = 1 + 5v + -1 + -5v

Reorder the terms:
12 + -15v + 4v2 = 1 + -1 + 5v + -5v

Combine like terms: 1 + -1 = 0
12 + -15v + 4v2 = 0 + 5v + -5v
12 + -15v + 4v2 = 5v + -5v

Combine like terms: 5v + -5v = 0
12 + -15v + 4v2 = 0

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

Divide each side by '4'.
3 + -3.75v + v2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3.75v + -3 + v2 = 0 + -3

Reorder the terms:
3 + -3 + -3.75v + v2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -3.75v + v2 = 0 + -3
-3.75v + v2 = 0 + -3

Combine like terms: 0 + -3 = -3
-3.75v + v2 = -3

The v term is -3.75v.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75v + 3.515625 + v2 = -3 + 3.515625

Reorder the terms:
3.515625 + -3.75v + v2 = -3 + 3.515625

Combine like terms: -3 + 3.515625 = 0.515625
3.515625 + -3.75v + v2 = 0.515625

Factor a perfect square on the left side:
(v + -1.875)(v + -1.875) = 0.515625

Calculate the square root of the right side: 0.718070331

Break this problem into two subproblems by setting 
(v + -1.875) equal to 0.718070331 and -0.718070331.

Subproblem 1
v + -1.875 = 0.718070331

Simplifying
v + -1.875 = 0.718070331

Reorder the terms:
-1.875 + v = 0.718070331

Solving
-1.875 + v = 0.718070331

Solving for variable 'v'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + v = 0.718070331 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + v = 0.718070331 + 1.875
v = 0.718070331 + 1.875

Combine like terms: 0.718070331 + 1.875 = 2.593070331
v = 2.593070331

Simplifying
v = 2.593070331

Subproblem 2
v + -1.875 = -0.718070331

Simplifying
v + -1.875 = -0.718070331

Reorder the terms:
-1.875 + v = -0.718070331

Solving
-1.875 + v = -0.718070331

Solving for variable 'v'.

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

Add '1.875' to each side of the equation.
-1.875 + 1.875 + v = -0.718070331 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + v = -0.718070331 + 1.875
v = -0.718070331 + 1.875

Combine like terms: -0.718070331 + 1.875 = 1.156929669
v = 1.156929669

Simplifying
v = 1.156929669

Solution
The solution to the problem is based on the solutions
from the subproblems.
v = {2.593070331, 1.156929669}