2v^2+9v-14=(v+4)(v+4)

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Solution for 2v^2+9v-14=(v+4)(v+4) equation: 


Simplifying
2v2 + 9v + -14 = (v + 4)(v + 4)

Reorder the terms:
-14 + 9v + 2v2 = (v + 4)(v + 4)

Reorder the terms:
-14 + 9v + 2v2 = (4 + v)(v + 4)

Reorder the terms:
-14 + 9v + 2v2 = (4 + v)(4 + v)

Multiply (4 + v) * (4 + v)
-14 + 9v + 2v2 = (4(4 + v) + v(4 + v))
-14 + 9v + 2v2 = ((4 * 4 + v * 4) + v(4 + v))
-14 + 9v + 2v2 = ((16 + 4v) + v(4 + v))
-14 + 9v + 2v2 = (16 + 4v + (4 * v + v * v))
-14 + 9v + 2v2 = (16 + 4v + (4v + v2))

Combine like terms: 4v + 4v = 8v
-14 + 9v + 2v2 = (16 + 8v + v2)

Solving
-14 + 9v + 2v2 = 16 + 8v + v2

Solving for variable 'v'.

Reorder the terms:
-14 + -16 + 9v + -8v + 2v2 + -1v2 = 16 + 8v + v2 + -16 + -8v + -1v2

Combine like terms: -14 + -16 = -30
-30 + 9v + -8v + 2v2 + -1v2 = 16 + 8v + v2 + -16 + -8v + -1v2

Combine like terms: 9v + -8v = 1v
-30 + 1v + 2v2 + -1v2 = 16 + 8v + v2 + -16 + -8v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
-30 + 1v + 1v2 = 16 + 8v + v2 + -16 + -8v + -1v2

Reorder the terms:
-30 + 1v + 1v2 = 16 + -16 + 8v + -8v + v2 + -1v2

Combine like terms: 16 + -16 = 0
-30 + 1v + 1v2 = 0 + 8v + -8v + v2 + -1v2
-30 + 1v + 1v2 = 8v + -8v + v2 + -1v2

Combine like terms: 8v + -8v = 0
-30 + 1v + 1v2 = 0 + v2 + -1v2
-30 + 1v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
-30 + 1v + 1v2 = 0

Factor a trinomial.
(-6 + -1v)(5 + -1v) = 0


Subproblem 1
Set the factor '(-6 + -1v)' equal to zero and attempt to solve:

Simplifying
-6 + -1v = 0

Solving
-6 + -1v = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1v = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1v = 0 + 6
-1v = 0 + 6

Combine like terms: 0 + 6 = 6
-1v = 6

Divide each side by '-1'.
v = -6

Simplifying
v = -6

Subproblem 2
Set the factor '(5 + -1v)' equal to zero and attempt to solve:

Simplifying
5 + -1v = 0

Solving
5 + -1v = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1v = 0 + -5

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

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

Divide each side by '-1'.
v = 5

Simplifying
v = 5
Solution
v = {-6, 5}

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