(v+1)(v+1)=2v^2+7v+7

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Solution for (v+1)(v+1)=2v^2+7v+7 equation: 


Simplifying
(v + 1)(v + 1) = 2v2 + 7v + 7

Reorder the terms:
(1 + v)(v + 1) = 2v2 + 7v + 7

Reorder the terms:
(1 + v)(1 + v) = 2v2 + 7v + 7

Multiply (1 + v) * (1 + v)
(1(1 + v) + v(1 + v)) = 2v2 + 7v + 7
((1 * 1 + v * 1) + v(1 + v)) = 2v2 + 7v + 7
((1 + 1v) + v(1 + v)) = 2v2 + 7v + 7
(1 + 1v + (1 * v + v * v)) = 2v2 + 7v + 7
(1 + 1v + (1v + v2)) = 2v2 + 7v + 7

Combine like terms: 1v + 1v = 2v
(1 + 2v + v2) = 2v2 + 7v + 7

Reorder the terms:
1 + 2v + v2 = 7 + 7v + 2v2

Solving
1 + 2v + v2 = 7 + 7v + 2v2

Solving for variable 'v'.

Reorder the terms:
1 + -7 + 2v + -7v + v2 + -2v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

Combine like terms: 1 + -7 = -6
-6 + 2v + -7v + v2 + -2v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

Combine like terms: 2v + -7v = -5v
-6 + -5v + v2 + -2v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-6 + -5v + -1v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

Reorder the terms:
-6 + -5v + -1v2 = 7 + -7 + 7v + -7v + 2v2 + -2v2

Combine like terms: 7 + -7 = 0
-6 + -5v + -1v2 = 0 + 7v + -7v + 2v2 + -2v2
-6 + -5v + -1v2 = 7v + -7v + 2v2 + -2v2

Combine like terms: 7v + -7v = 0
-6 + -5v + -1v2 = 0 + 2v2 + -2v2
-6 + -5v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-6 + -5v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 5v + v2) = 0

Factor a trinomial.
-1((3 + v)(2 + v)) = 0

Ignore the factor -1.

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

Simplifying
3 + v = 0

Solving
3 + v = 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 + v = 0 + -3

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

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

Simplifying
v = -3

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

Add '-2' to each side of the equation.
2 + -2 + v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + v = 0 + -2
v = 0 + -2

Combine like terms: 0 + -2 = -2
v = -2

Simplifying
v = -2
Solution
v = {-3, -2}

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