2v^2+8v-17=(v+2)(v+2)

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Solution for 2v^2+8v-17=(v+2)(v+2) equation: 


Simplifying
2v2 + 8v + -17 = (v + 2)(v + 2)

Reorder the terms:
-17 + 8v + 2v2 = (v + 2)(v + 2)

Reorder the terms:
-17 + 8v + 2v2 = (2 + v)(v + 2)

Reorder the terms:
-17 + 8v + 2v2 = (2 + v)(2 + v)

Multiply (2 + v) * (2 + v)
-17 + 8v + 2v2 = (2(2 + v) + v(2 + v))
-17 + 8v + 2v2 = ((2 * 2 + v * 2) + v(2 + v))
-17 + 8v + 2v2 = ((4 + 2v) + v(2 + v))
-17 + 8v + 2v2 = (4 + 2v + (2 * v + v * v))
-17 + 8v + 2v2 = (4 + 2v + (2v + v2))

Combine like terms: 2v + 2v = 4v
-17 + 8v + 2v2 = (4 + 4v + v2)

Solving
-17 + 8v + 2v2 = 4 + 4v + v2

Solving for variable 'v'.

Reorder the terms:
-17 + -4 + 8v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: -17 + -4 = -21
-21 + 8v + -4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 8v + -4v = 4v
-21 + 4v + 2v2 + -1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-21 + 4v + 1v2 = 4 + 4v + v2 + -4 + -4v + -1v2

Reorder the terms:
-21 + 4v + 1v2 = 4 + -4 + 4v + -4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
-21 + 4v + 1v2 = 0 + 4v + -4v + v2 + -1v2
-21 + 4v + 1v2 = 4v + -4v + v2 + -1v2

Combine like terms: 4v + -4v = 0
-21 + 4v + 1v2 = 0 + v2 + -1v2
-21 + 4v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-21 + 4v + 1v2 = 0

Factor a trinomial.
(-7 + -1v)(3 + -1v) = 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 '(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
Solution
v = {-7, 3}

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