2v^2+11v+34=(v+6)(v+6)

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Solution for 2v^2+11v+34=(v+6)(v+6) equation: 


Simplifying
2v2 + 11v + 34 = (v + 6)(v + 6)

Reorder the terms:
34 + 11v + 2v2 = (v + 6)(v + 6)

Reorder the terms:
34 + 11v + 2v2 = (6 + v)(v + 6)

Reorder the terms:
34 + 11v + 2v2 = (6 + v)(6 + v)

Multiply (6 + v) * (6 + v)
34 + 11v + 2v2 = (6(6 + v) + v(6 + v))
34 + 11v + 2v2 = ((6 * 6 + v * 6) + v(6 + v))
34 + 11v + 2v2 = ((36 + 6v) + v(6 + v))
34 + 11v + 2v2 = (36 + 6v + (6 * v + v * v))
34 + 11v + 2v2 = (36 + 6v + (6v + v2))

Combine like terms: 6v + 6v = 12v
34 + 11v + 2v2 = (36 + 12v + v2)

Solving
34 + 11v + 2v2 = 36 + 12v + v2

Solving for variable 'v'.

Reorder the terms:
34 + -36 + 11v + -12v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 34 + -36 = -2
-2 + 11v + -12v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 11v + -12v = -1v
-2 + -1v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-2 + -1v + 1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Reorder the terms:
-2 + -1v + 1v2 = 36 + -36 + 12v + -12v + v2 + -1v2

Combine like terms: 36 + -36 = 0
-2 + -1v + 1v2 = 0 + 12v + -12v + v2 + -1v2
-2 + -1v + 1v2 = 12v + -12v + v2 + -1v2

Combine like terms: 12v + -12v = 0
-2 + -1v + 1v2 = 0 + v2 + -1v2
-2 + -1v + 1v2 = v2 + -1v2

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

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


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

Simplifying
-1 + -1v = 0

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

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

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

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

Simplifying
v = -1

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

Simplifying
2 + -1v = 0

Solving
2 + -1v = 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 + -1v = 0 + -2

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

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

Divide each side by '-1'.
v = 2

Simplifying
v = 2
Solution
v = {-1, 2}

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