(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.
(6 + -1v)(4 + v) = 0


Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve:

Simplifying
6 + -1v = 0

Solving
6 + -1v = 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 + -1v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1v = 0 + -6
-1v = 0 + -6

Combine like terms: 0 + -6 = -6
-1v = -6

Divide each side by '-1'.
v = 6

Simplifying
v = 6

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

Simplifying
4 + v = 0

Solving
4 + v = 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 + v = 0 + -4

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

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

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

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