(v+4)(v+4)=2v^2+11v+18

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Solution for (v+4)(v+4)=2v^2+11v+18 equation: 


Simplifying
(v + 4)(v + 4) = 2v2 + 11v + 18

Reorder the terms:
(4 + v)(v + 4) = 2v2 + 11v + 18

Reorder the terms:
(4 + v)(4 + v) = 2v2 + 11v + 18

Multiply (4 + v) * (4 + v)
(4(4 + v) + v(4 + v)) = 2v2 + 11v + 18
((4 * 4 + v * 4) + v(4 + v)) = 2v2 + 11v + 18
((16 + 4v) + v(4 + v)) = 2v2 + 11v + 18
(16 + 4v + (4 * v + v * v)) = 2v2 + 11v + 18
(16 + 4v + (4v + v2)) = 2v2 + 11v + 18

Combine like terms: 4v + 4v = 8v
(16 + 8v + v2) = 2v2 + 11v + 18

Reorder the terms:
16 + 8v + v2 = 18 + 11v + 2v2

Solving
16 + 8v + v2 = 18 + 11v + 2v2

Solving for variable 'v'.

Reorder the terms:
16 + -18 + 8v + -11v + v2 + -2v2 = 18 + 11v + 2v2 + -18 + -11v + -2v2

Combine like terms: 16 + -18 = -2
-2 + 8v + -11v + v2 + -2v2 = 18 + 11v + 2v2 + -18 + -11v + -2v2

Combine like terms: 8v + -11v = -3v
-2 + -3v + v2 + -2v2 = 18 + 11v + 2v2 + -18 + -11v + -2v2

Combine like terms: v2 + -2v2 = -1v2
-2 + -3v + -1v2 = 18 + 11v + 2v2 + -18 + -11v + -2v2

Reorder the terms:
-2 + -3v + -1v2 = 18 + -18 + 11v + -11v + 2v2 + -2v2

Combine like terms: 18 + -18 = 0
-2 + -3v + -1v2 = 0 + 11v + -11v + 2v2 + -2v2
-2 + -3v + -1v2 = 11v + -11v + 2v2 + -2v2

Combine like terms: 11v + -11v = 0
-2 + -3v + -1v2 = 0 + 2v2 + -2v2
-2 + -3v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
-2 + -3v + -1v2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 3v + v2) = 0

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

Ignore the factor -1.

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

Simplifying
2 + v = 0

Solving
2 + v = 0

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

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

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

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

Simplifying
v = -2

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 = {-2, -1}

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