2v^2+7v+61=(v+7)(v+7)

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Solution for 2v^2+7v+61=(v+7)(v+7) equation:


Simplifying
2v2 + 7v + 61 = (v + 7)(v + 7)

Reorder the terms:
61 + 7v + 2v2 = (v + 7)(v + 7)

Reorder the terms:
61 + 7v + 2v2 = (7 + v)(v + 7)

Reorder the terms:
61 + 7v + 2v2 = (7 + v)(7 + v)

Multiply (7 + v) * (7 + v)
61 + 7v + 2v2 = (7(7 + v) + v(7 + v))
61 + 7v + 2v2 = ((7 * 7 + v * 7) + v(7 + v))
61 + 7v + 2v2 = ((49 + 7v) + v(7 + v))
61 + 7v + 2v2 = (49 + 7v + (7 * v + v * v))
61 + 7v + 2v2 = (49 + 7v + (7v + v2))

Combine like terms: 7v + 7v = 14v
61 + 7v + 2v2 = (49 + 14v + v2)

Solving
61 + 7v + 2v2 = 49 + 14v + v2

Solving for variable 'v'.

Reorder the terms:
61 + -49 + 7v + -14v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 61 + -49 = 12
12 + 7v + -14v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 7v + -14v = -7v
12 + -7v + 2v2 + -1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
12 + -7v + 1v2 = 49 + 14v + v2 + -49 + -14v + -1v2

Reorder the terms:
12 + -7v + 1v2 = 49 + -49 + 14v + -14v + v2 + -1v2

Combine like terms: 49 + -49 = 0
12 + -7v + 1v2 = 0 + 14v + -14v + v2 + -1v2
12 + -7v + 1v2 = 14v + -14v + v2 + -1v2

Combine like terms: 14v + -14v = 0
12 + -7v + 1v2 = 0 + v2 + -1v2
12 + -7v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
12 + -7v + 1v2 = 0

Factor a trinomial.
(3 + -1v)(4 + -1v) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve:

Simplifying
4 + -1v = 0

Solving
4 + -1v = 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 + -1v = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1v = 0 + -4
-1v = 0 + -4

Combine like terms: 0 + -4 = -4
-1v = -4

Divide each side by '-1'.
v = 4

Simplifying
v = 4
Solution
v = {3, 4}

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