(v+6)(v+6)=2v^2+6v+29

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Solution for (v+6)(v+6)=2v^2+6v+29 equation: 


Simplifying
(v + 6)(v + 6) = 2v2 + 6v + 29

Reorder the terms:
(6 + v)(v + 6) = 2v2 + 6v + 29

Reorder the terms:
(6 + v)(6 + v) = 2v2 + 6v + 29

Multiply (6 + v) * (6 + v)
(6(6 + v) + v(6 + v)) = 2v2 + 6v + 29
((6 * 6 + v * 6) + v(6 + v)) = 2v2 + 6v + 29
((36 + 6v) + v(6 + v)) = 2v2 + 6v + 29
(36 + 6v + (6 * v + v * v)) = 2v2 + 6v + 29
(36 + 6v + (6v + v2)) = 2v2 + 6v + 29

Combine like terms: 6v + 6v = 12v
(36 + 12v + v2) = 2v2 + 6v + 29

Reorder the terms:
36 + 12v + v2 = 29 + 6v + 2v2

Solving
36 + 12v + v2 = 29 + 6v + 2v2

Solving for variable 'v'.

Reorder the terms:
36 + -29 + 12v + -6v + v2 + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2

Combine like terms: 36 + -29 = 7
7 + 12v + -6v + v2 + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2

Combine like terms: 12v + -6v = 6v
7 + 6v + v2 + -2v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2

Combine like terms: v2 + -2v2 = -1v2
7 + 6v + -1v2 = 29 + 6v + 2v2 + -29 + -6v + -2v2

Reorder the terms:
7 + 6v + -1v2 = 29 + -29 + 6v + -6v + 2v2 + -2v2

Combine like terms: 29 + -29 = 0
7 + 6v + -1v2 = 0 + 6v + -6v + 2v2 + -2v2
7 + 6v + -1v2 = 6v + -6v + 2v2 + -2v2

Combine like terms: 6v + -6v = 0
7 + 6v + -1v2 = 0 + 2v2 + -2v2
7 + 6v + -1v2 = 2v2 + -2v2

Combine like terms: 2v2 + -2v2 = 0
7 + 6v + -1v2 = 0

Factor a trinomial.
(7 + -1v)(1 + v) = 0


Subproblem 1
Set the factor '(7 + -1v)' equal to zero and attempt to solve:

Simplifying
7 + -1v = 0

Solving
7 + -1v = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1v = 0 + -7
-1v = 0 + -7

Combine like terms: 0 + -7 = -7
-1v = -7

Divide each side by '-1'.
v = 7

Simplifying
v = 7

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 = {7, -1}

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