v^2+2v+1=3v+13

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Solution for v^2+2v+1=3v+13 equation:


Simplifying
v2 + 2v + 1 = 3v + 13

Reorder the terms:
1 + 2v + v2 = 3v + 13

Reorder the terms:
1 + 2v + v2 = 13 + 3v

Solving
1 + 2v + v2 = 13 + 3v

Solving for variable 'v'.

Reorder the terms:
1 + -13 + 2v + -3v + v2 = 13 + 3v + -13 + -3v

Combine like terms: 1 + -13 = -12
-12 + 2v + -3v + v2 = 13 + 3v + -13 + -3v

Combine like terms: 2v + -3v = -1v
-12 + -1v + v2 = 13 + 3v + -13 + -3v

Reorder the terms:
-12 + -1v + v2 = 13 + -13 + 3v + -3v

Combine like terms: 13 + -13 = 0
-12 + -1v + v2 = 0 + 3v + -3v
-12 + -1v + v2 = 3v + -3v

Combine like terms: 3v + -3v = 0
-12 + -1v + v2 = 0

Factor a trinomial.
(-3 + -1v)(4 + -1v) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {-3, 4}

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