(v-4)(v-4)=2v^2-12v+11

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Solution for (v-4)(v-4)=2v^2-12v+11 equation: 


Simplifying
(v + -4)(v + -4) = 2v2 + -12v + 11

Reorder the terms:
(-4 + v)(v + -4) = 2v2 + -12v + 11

Reorder the terms:
(-4 + v)(-4 + v) = 2v2 + -12v + 11

Multiply (-4 + v) * (-4 + v)
(-4(-4 + v) + v(-4 + v)) = 2v2 + -12v + 11
((-4 * -4 + v * -4) + v(-4 + v)) = 2v2 + -12v + 11
((16 + -4v) + v(-4 + v)) = 2v2 + -12v + 11
(16 + -4v + (-4 * v + v * v)) = 2v2 + -12v + 11
(16 + -4v + (-4v + v2)) = 2v2 + -12v + 11

Combine like terms: -4v + -4v = -8v
(16 + -8v + v2) = 2v2 + -12v + 11

Reorder the terms:
16 + -8v + v2 = 11 + -12v + 2v2

Solving
16 + -8v + v2 = 11 + -12v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -11 + -8v + 12v + v2 + -2v2 = 11 + -12v + 2v2 + -11 + 12v + -2v2

Combine like terms: 16 + -11 = 5
5 + -8v + 12v + v2 + -2v2 = 11 + -12v + 2v2 + -11 + 12v + -2v2

Combine like terms: -8v + 12v = 4v
5 + 4v + v2 + -2v2 = 11 + -12v + 2v2 + -11 + 12v + -2v2

Combine like terms: v2 + -2v2 = -1v2
5 + 4v + -1v2 = 11 + -12v + 2v2 + -11 + 12v + -2v2

Reorder the terms:
5 + 4v + -1v2 = 11 + -11 + -12v + 12v + 2v2 + -2v2

Combine like terms: 11 + -11 = 0
5 + 4v + -1v2 = 0 + -12v + 12v + 2v2 + -2v2
5 + 4v + -1v2 = -12v + 12v + 2v2 + -2v2

Combine like terms: -12v + 12v = 0
5 + 4v + -1v2 = 0 + 2v2 + -2v2
5 + 4v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
5 + 4v + -1v2 = 0

Factor a trinomial.
(5 + -1v)(1 + v) = 0


Subproblem 1
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1v = 0 + -5
-1v = 0 + -5

Combine like terms: 0 + -5 = -5
-1v = -5

Divide each side by '-1'.
v = 5

Simplifying
v = 5

Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve:

Simplifying
1 + v = 0

Solving
1 + v = 0

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

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

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

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

Simplifying
v = -1
Solution
v = {5, -1}

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