(v+3)(v+3)=2v^2-2v+24

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Solution for (v+3)(v+3)=2v^2-2v+24 equation: 


Simplifying
(v + 3)(v + 3) = 2v2 + -2v + 24

Reorder the terms:
(3 + v)(v + 3) = 2v2 + -2v + 24

Reorder the terms:
(3 + v)(3 + v) = 2v2 + -2v + 24

Multiply (3 + v) * (3 + v)
(3(3 + v) + v(3 + v)) = 2v2 + -2v + 24
((3 * 3 + v * 3) + v(3 + v)) = 2v2 + -2v + 24
((9 + 3v) + v(3 + v)) = 2v2 + -2v + 24
(9 + 3v + (3 * v + v * v)) = 2v2 + -2v + 24
(9 + 3v + (3v + v2)) = 2v2 + -2v + 24

Combine like terms: 3v + 3v = 6v
(9 + 6v + v2) = 2v2 + -2v + 24

Reorder the terms:
9 + 6v + v2 = 24 + -2v + 2v2

Solving
9 + 6v + v2 = 24 + -2v + 2v2

Solving for variable 'v'.

Reorder the terms:
9 + -24 + 6v + 2v + v2 + -2v2 = 24 + -2v + 2v2 + -24 + 2v + -2v2

Combine like terms: 9 + -24 = -15
-15 + 6v + 2v + v2 + -2v2 = 24 + -2v + 2v2 + -24 + 2v + -2v2

Combine like terms: 6v + 2v = 8v
-15 + 8v + v2 + -2v2 = 24 + -2v + 2v2 + -24 + 2v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-15 + 8v + -1v2 = 24 + -2v + 2v2 + -24 + 2v + -2v2

Reorder the terms:
-15 + 8v + -1v2 = 24 + -24 + -2v + 2v + 2v2 + -2v2

Combine like terms: 24 + -24 = 0
-15 + 8v + -1v2 = 0 + -2v + 2v + 2v2 + -2v2
-15 + 8v + -1v2 = -2v + 2v + 2v2 + -2v2

Combine like terms: -2v + 2v = 0
-15 + 8v + -1v2 = 0 + 2v2 + -2v2
-15 + 8v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-15 + 8v + -1v2 = 0

Factor a trinomial.
(-5 + v)(3 + -1v) = 0


Subproblem 1
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

Subproblem 2
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
Solution
v = {5, 3}

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