(v+2)(v+2)=2v^2+6v-20

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Solution for (v+2)(v+2)=2v^2+6v-20 equation: 


Simplifying
(v + 2)(v + 2) = 2v2 + 6v + -20

Reorder the terms:
(2 + v)(v + 2) = 2v2 + 6v + -20

Reorder the terms:
(2 + v)(2 + v) = 2v2 + 6v + -20

Multiply (2 + v) * (2 + v)
(2(2 + v) + v(2 + v)) = 2v2 + 6v + -20
((2 * 2 + v * 2) + v(2 + v)) = 2v2 + 6v + -20
((4 + 2v) + v(2 + v)) = 2v2 + 6v + -20
(4 + 2v + (2 * v + v * v)) = 2v2 + 6v + -20
(4 + 2v + (2v + v2)) = 2v2 + 6v + -20

Combine like terms: 2v + 2v = 4v
(4 + 4v + v2) = 2v2 + 6v + -20

Reorder the terms:
4 + 4v + v2 = -20 + 6v + 2v2

Solving
4 + 4v + v2 = -20 + 6v + 2v2

Solving for variable 'v'.

Reorder the terms:
4 + 20 + 4v + -6v + v2 + -2v2 = -20 + 6v + 2v2 + 20 + -6v + -2v2

Combine like terms: 4 + 20 = 24
24 + 4v + -6v + v2 + -2v2 = -20 + 6v + 2v2 + 20 + -6v + -2v2

Combine like terms: 4v + -6v = -2v
24 + -2v + v2 + -2v2 = -20 + 6v + 2v2 + 20 + -6v + -2v2

Combine like terms: v2 + -2v2 = -1v2
24 + -2v + -1v2 = -20 + 6v + 2v2 + 20 + -6v + -2v2

Reorder the terms:
24 + -2v + -1v2 = -20 + 20 + 6v + -6v + 2v2 + -2v2

Combine like terms: -20 + 20 = 0
24 + -2v + -1v2 = 0 + 6v + -6v + 2v2 + -2v2
24 + -2v + -1v2 = 6v + -6v + 2v2 + -2v2

Combine like terms: 6v + -6v = 0
24 + -2v + -1v2 = 0 + 2v2 + -2v2
24 + -2v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
24 + -2v + -1v2 = 0

Factor a trinomial.
(4 + -1v)(6 + v) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

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

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6
Solution
v = {4, -6}

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