2v^2+7v+40=(v+6)(v+6)

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Solution for 2v^2+7v+40=(v+6)(v+6) equation: 


Simplifying
2v2 + 7v + 40 = (v + 6)(v + 6)

Reorder the terms:
40 + 7v + 2v2 = (v + 6)(v + 6)

Reorder the terms:
40 + 7v + 2v2 = (6 + v)(v + 6)

Reorder the terms:
40 + 7v + 2v2 = (6 + v)(6 + v)

Multiply (6 + v) * (6 + v)
40 + 7v + 2v2 = (6(6 + v) + v(6 + v))
40 + 7v + 2v2 = ((6 * 6 + v * 6) + v(6 + v))
40 + 7v + 2v2 = ((36 + 6v) + v(6 + v))
40 + 7v + 2v2 = (36 + 6v + (6 * v + v * v))
40 + 7v + 2v2 = (36 + 6v + (6v + v2))

Combine like terms: 6v + 6v = 12v
40 + 7v + 2v2 = (36 + 12v + v2)

Solving
40 + 7v + 2v2 = 36 + 12v + v2

Solving for variable 'v'.

Reorder the terms:
40 + -36 + 7v + -12v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 40 + -36 = 4
4 + 7v + -12v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 7v + -12v = -5v
4 + -5v + 2v2 + -1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
4 + -5v + 1v2 = 36 + 12v + v2 + -36 + -12v + -1v2

Reorder the terms:
4 + -5v + 1v2 = 36 + -36 + 12v + -12v + v2 + -1v2

Combine like terms: 36 + -36 = 0
4 + -5v + 1v2 = 0 + 12v + -12v + v2 + -1v2
4 + -5v + 1v2 = 12v + -12v + v2 + -1v2

Combine like terms: 12v + -12v = 0
4 + -5v + 1v2 = 0 + v2 + -1v2
4 + -5v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
4 + -5v + 1v2 = 0

Factor a trinomial.
(1 + -1v)(4 + -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 '(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 = {1, 4}

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