(v+3)(v+3)=2v^2+7v+7

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Solution for (v+3)(v+3)=2v^2+7v+7 equation: 


Simplifying
(v + 3)(v + 3) = 2v2 + 7v + 7

Reorder the terms:
(3 + v)(v + 3) = 2v2 + 7v + 7

Reorder the terms:
(3 + v)(3 + v) = 2v2 + 7v + 7

Multiply (3 + v) * (3 + v)
(3(3 + v) + v(3 + v)) = 2v2 + 7v + 7
((3 * 3 + v * 3) + v(3 + v)) = 2v2 + 7v + 7
((9 + 3v) + v(3 + v)) = 2v2 + 7v + 7
(9 + 3v + (3 * v + v * v)) = 2v2 + 7v + 7
(9 + 3v + (3v + v2)) = 2v2 + 7v + 7

Combine like terms: 3v + 3v = 6v
(9 + 6v + v2) = 2v2 + 7v + 7

Reorder the terms:
9 + 6v + v2 = 7 + 7v + 2v2

Solving
9 + 6v + v2 = 7 + 7v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + -7 + 6v + -7v + v2 + -2v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

Combine like terms: 9 + -7 = 2
2 + 6v + -7v + v2 + -2v2 = 7 + 7v + 2v2 + -7 + -7v + -2v2

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

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

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

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

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

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

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


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

Simplifying
1 + -1v = 0

Solving
1 + -1v = 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 + -1v = 0 + -1

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

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

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

Simplifying
v = 1

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 = {1, -2}

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