v^2+v+5=(3v+2)(v-4)

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Solution for v^2+v+5=(3v+2)(v-4) equation: 


Simplifying
v2 + v + 5 = (3v + 2)(v + -4)

Reorder the terms:
5 + v + v2 = (3v + 2)(v + -4)

Reorder the terms:
5 + v + v2 = (2 + 3v)(v + -4)

Reorder the terms:
5 + v + v2 = (2 + 3v)(-4 + v)

Multiply (2 + 3v) * (-4 + v)
5 + v + v2 = (2(-4 + v) + 3v * (-4 + v))
5 + v + v2 = ((-4 * 2 + v * 2) + 3v * (-4 + v))
5 + v + v2 = ((-8 + 2v) + 3v * (-4 + v))
5 + v + v2 = (-8 + 2v + (-4 * 3v + v * 3v))
5 + v + v2 = (-8 + 2v + (-12v + 3v2))

Combine like terms: 2v + -12v = -10v
5 + v + v2 = (-8 + -10v + 3v2)

Solving
5 + v + v2 = -8 + -10v + 3v2

Solving for variable 'v'.

Reorder the terms:
5 + 8 + v + 10v + v2 + -3v2 = -8 + -10v + 3v2 + 8 + 10v + -3v2

Combine like terms: 5 + 8 = 13
13 + v + 10v + v2 + -3v2 = -8 + -10v + 3v2 + 8 + 10v + -3v2

Combine like terms: v + 10v = 11v
13 + 11v + v2 + -3v2 = -8 + -10v + 3v2 + 8 + 10v + -3v2

Combine like terms: v2 + -3v2 = -2v2
13 + 11v + -2v2 = -8 + -10v + 3v2 + 8 + 10v + -3v2

Reorder the terms:
13 + 11v + -2v2 = -8 + 8 + -10v + 10v + 3v2 + -3v2

Combine like terms: -8 + 8 = 0
13 + 11v + -2v2 = 0 + -10v + 10v + 3v2 + -3v2
13 + 11v + -2v2 = -10v + 10v + 3v2 + -3v2

Combine like terms: -10v + 10v = 0
13 + 11v + -2v2 = 0 + 3v2 + -3v2
13 + 11v + -2v2 = 3v2 + -3v2

Combine like terms: 3v2 + -3v2 = 0
13 + 11v + -2v2 = 0

Factor a trinomial.
(13 + -2v)(1 + v) = 0


Subproblem 1
Set the factor '(13 + -2v)' equal to zero and attempt to solve:

Simplifying
13 + -2v = 0

Solving
13 + -2v = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2v = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2v = 0 + -13
-2v = 0 + -13

Combine like terms: 0 + -13 = -13
-2v = -13

Divide each side by '-2'.
v = 6.5

Simplifying
v = 6.5

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

Simplifying
1 + v = 0

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

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

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

Simplifying
v = -1
Solution
v = {6.5, -1}

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