(v+3)(v+3)=2v^2+9v-1

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Solution for (v+3)(v+3)=2v^2+9v-1 equation: 


Simplifying
(v + 3)(v + 3) = 2v2 + 9v + -1

Reorder the terms:
(3 + v)(v + 3) = 2v2 + 9v + -1

Reorder the terms:
(3 + v)(3 + v) = 2v2 + 9v + -1

Multiply (3 + v) * (3 + v)
(3(3 + v) + v(3 + v)) = 2v2 + 9v + -1
((3 * 3 + v * 3) + v(3 + v)) = 2v2 + 9v + -1
((9 + 3v) + v(3 + v)) = 2v2 + 9v + -1
(9 + 3v + (3 * v + v * v)) = 2v2 + 9v + -1
(9 + 3v + (3v + v2)) = 2v2 + 9v + -1

Combine like terms: 3v + 3v = 6v
(9 + 6v + v2) = 2v2 + 9v + -1

Reorder the terms:
9 + 6v + v2 = -1 + 9v + 2v2

Solving
9 + 6v + v2 = -1 + 9v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + 1 + 6v + -9v + v2 + -2v2 = -1 + 9v + 2v2 + 1 + -9v + -2v2

Combine like terms: 9 + 1 = 10
10 + 6v + -9v + v2 + -2v2 = -1 + 9v + 2v2 + 1 + -9v + -2v2

Combine like terms: 6v + -9v = -3v
10 + -3v + v2 + -2v2 = -1 + 9v + 2v2 + 1 + -9v + -2v2

Combine like terms: v2 + -2v2 = -1v2
10 + -3v + -1v2 = -1 + 9v + 2v2 + 1 + -9v + -2v2

Reorder the terms:
10 + -3v + -1v2 = -1 + 1 + 9v + -9v + 2v2 + -2v2

Combine like terms: -1 + 1 = 0
10 + -3v + -1v2 = 0 + 9v + -9v + 2v2 + -2v2
10 + -3v + -1v2 = 9v + -9v + 2v2 + -2v2

Combine like terms: 9v + -9v = 0
10 + -3v + -1v2 = 0 + 2v2 + -2v2
10 + -3v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
10 + -3v + -1v2 = 0

Factor a trinomial.
(2 + -1v)(5 + v) = 0


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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 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 + -1v = 0 + -2

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

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

Divide each side by '-1'.
v = 2

Simplifying
v = 2

Subproblem 2
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
Solution
v = {2, -5}

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