(v+1)(v+1)=2v^2-6v+16

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Solution for (v+1)(v+1)=2v^2-6v+16 equation: 


Simplifying
(v + 1)(v + 1) = 2v2 + -6v + 16

Reorder the terms:
(1 + v)(v + 1) = 2v2 + -6v + 16

Reorder the terms:
(1 + v)(1 + v) = 2v2 + -6v + 16

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

Combine like terms: 1v + 1v = 2v
(1 + 2v + v2) = 2v2 + -6v + 16

Reorder the terms:
1 + 2v + v2 = 16 + -6v + 2v2

Solving
1 + 2v + v2 = 16 + -6v + 2v2

Solving for variable 'v'.

Reorder the terms:
1 + -16 + 2v + 6v + v2 + -2v2 = 16 + -6v + 2v2 + -16 + 6v + -2v2

Combine like terms: 1 + -16 = -15
-15 + 2v + 6v + v2 + -2v2 = 16 + -6v + 2v2 + -16 + 6v + -2v2

Combine like terms: 2v + 6v = 8v
-15 + 8v + v2 + -2v2 = 16 + -6v + 2v2 + -16 + 6v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-15 + 8v + -1v2 = 16 + -6v + 2v2 + -16 + 6v + -2v2

Reorder the terms:
-15 + 8v + -1v2 = 16 + -16 + -6v + 6v + 2v2 + -2v2

Combine like terms: 16 + -16 = 0
-15 + 8v + -1v2 = 0 + -6v + 6v + 2v2 + -2v2
-15 + 8v + -1v2 = -6v + 6v + 2v2 + -2v2

Combine like terms: -6v + 6v = 0
-15 + 8v + -1v2 = 0 + 2v2 + -2v2
-15 + 8v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-15 + 8v + -1v2 = 0

Factor a trinomial.
(-5 + v)(3 + -1v) = 0


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

Simplifying
-5 + v = 0

Solving
-5 + v = 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 + v = 0 + 5

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

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

Simplifying
v = 5

Subproblem 2
Set the factor '(3 + -1v)' equal to zero and attempt to solve:

Simplifying
3 + -1v = 0

Solving
3 + -1v = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1v = 0 + -3

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

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

Divide each side by '-1'.
v = 3

Simplifying
v = 3
Solution
v = {5, 3}

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